File: reduce%40useless-runes.lsp

package info (click to toggle)
acl2 8.6%2Bdfsg-2
links: PTS
area: main
in suites: trixie
size: 1,111,420 kB
sloc: lisp: 17,818,294; java: 125,359; python: 28,122; javascript: 23,458; cpp: 18,851; ansic: 11,569; perl: 7,678; xml: 5,591; sh: 3,976; makefile: 3,833; ruby: 2,633; yacc: 1,126; ml: 763; awk: 295; csh: 233; lex: 197; php: 178; tcl: 49; asm: 23; haskell: 17
file content (6491 lines) | stat: -rw-r--r-- 290,194 bytes
parent folder | download | duplicates (2)
(DM::DISTINCT-SYMBOLS-ATOM
 (176 88 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (176 88 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (94 94 (:TYPE-PRESCRIPTION DM::TRIPP))
 (94 94 (:TYPE-PRESCRIPTION DM::ECP))
 (15 15 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE DM::PERM-MEMBER))
 (12 6 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (12 6 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (10 10 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal c (- x))|))
 (7 7 (:REWRITE |(equal (/ x) c)|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) c)|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 )
(DM::ALL-INTEGERS-INTEGER
 (48 24 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (48 24 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (36 36 (:TYPE-PRESCRIPTION DM::TRIPP))
 (36 36 (:TYPE-PRESCRIPTION DM::ECP))
 (18 11 (:REWRITE DEFAULT-LESS-THAN-2))
 (18 6 (:REWRITE DM::INTEGERP-EC-X))
 (18 6 (:REWRITE DM::INT-CAR-TRIPP))
 (17 10 (:REWRITE DEFAULT-PLUS-2))
 (14 10 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (14 8 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (13 8 (:REWRITE SIMPLIFY-SUMS-<))
 (11 11 (:REWRITE THE-FLOOR-BELOW))
 (11 11 (:REWRITE THE-FLOOR-ABOVE))
 (11 11 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (11 11 (:REWRITE REDUCE-INTEGERP-+))
 (11 11 (:REWRITE INTEGERP-MINUS-X))
 (11 11 (:REWRITE DEFAULT-LESS-THAN-1))
 (11 11 (:META META-INTEGERP-CORRECT))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE INTEGERP-<-CONSTANT))
 (10 10 (:REWRITE DEFAULT-PLUS-1))
 (10 10 (:REWRITE CONSTANT-<-INTEGERP))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (- x))|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) (/ y))|))
 (10 10 (:REWRITE |(< (- x) c)|))
 (10 10 (:REWRITE |(< (- x) (- y))|))
 (9 9 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 1 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 )
(DM::ALL-INTEGERS-NTHCDR
 (70 8 (:REWRITE ZP-OPEN))
 (45 45 (:TYPE-PRESCRIPTION DM::ECP))
 (37 37 (:TYPE-PRESCRIPTION DM::TRIPP))
 (33 11 (:REWRITE DM::INTEGERP-EC-X))
 (33 11 (:REWRITE DM::INT-CAR-TRIPP))
 (30 15 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (30 15 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (30 2 (:REWRITE |(+ (+ x y) z)|))
 (20 20 (:REWRITE DEFAULT-PLUS-2))
 (20 20 (:REWRITE DEFAULT-PLUS-1))
 (16 8 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (12 12 (:REWRITE DEFAULT-CAR))
 (11 11 (:REWRITE REDUCE-INTEGERP-+))
 (11 11 (:REWRITE INTEGERP-MINUS-X))
 (11 11 (:META META-INTEGERP-CORRECT))
 (10 10 (:REWRITE DEFAULT-CDR))
 (10 2 (:REWRITE |(+ c (+ d x))|))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (9 9 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 )
(DM::NTHCDR+
 (566 283 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (283 283 (:TYPE-PRESCRIPTION DM::ECP))
 (264 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (186 6 (:REWRITE ACL2-NUMBERP-X))
 (106 13 (:REWRITE ZP-OPEN))
 (90 3 (:REWRITE RATIONALP-X))
 (86 14 (:REWRITE DEFAULT-CDR))
 (84 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (55 55 (:REWRITE DEFAULT-PLUS-2))
 (55 55 (:REWRITE DEFAULT-PLUS-1))
 (28 28 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (28 28 (:REWRITE NORMALIZE-ADDENDS))
 (12 7 (:REWRITE |(+ c (+ d x))|))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (10 10 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE INTEGERP-<-CONSTANT))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-1))
 (10 10 (:REWRITE CONSTANT-<-INTEGERP))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (- x))|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) (/ y))|))
 (10 10 (:REWRITE |(< (- x) c)|))
 (10 10 (:REWRITE |(< (- x) (- y))|))
 (9 9 (:REWRITE SIMPLIFY-SUMS-<))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:META META-INTEGERP-CORRECT))
 (7 7 (:REWRITE |(< (/ x) 0)|))
 (7 7 (:REWRITE |(< (* x y) 0)|))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (3 3 (:REWRITE REDUCE-RATIONALP-+))
 (3 3 (:REWRITE REDUCE-RATIONALP-*))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE RATIONALP-MINUS-X))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE |(equal c (/ x))|))
 (3 3 (:REWRITE |(equal c (- x))|))
 (3 3 (:REWRITE |(equal (/ x) c)|))
 (3 3 (:REWRITE |(equal (/ x) (/ y))|))
 (3 3 (:REWRITE |(equal (- x) c)|))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (3 3 (:REWRITE |(< y (+ (- c) x))|))
 (3 3 (:REWRITE |(< x (+ c/d y))|))
 (3 3 (:REWRITE |(< 0 (/ x))|))
 (3 3 (:REWRITE |(< 0 (* x y))|))
 (3 3 (:META META-RATIONALP-CORRECT))
 )
(DM::CAR-NTHCDR
 (852 426 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (710 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (620 620 (:TYPE-PRESCRIPTION DM::ECP))
 (530 14 (:REWRITE ACL2-NUMBERP-X))
 (364 182 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (308 7 (:REWRITE RATIONALP-X))
 (200 14 (:REWRITE ZP-OPEN))
 (194 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (85 16 (:REWRITE DEFAULT-CAR))
 (70 2 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (64 2 (:DEFINITION DM::ALL-INTEGERS))
 (36 36 (:REWRITE DEFAULT-PLUS-2))
 (36 36 (:REWRITE DEFAULT-PLUS-1))
 (30 6 (:REWRITE |(+ c (+ d x))|))
 (30 2 (:REWRITE |(+ (+ x y) z)|))
 (22 22 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (22 22 (:REWRITE NORMALIZE-ADDENDS))
 (19 7 (:REWRITE DM::INTEGERP-EC-X))
 (19 7 (:REWRITE DM::INT-CAR-TRIPP))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:META META-INTEGERP-CORRECT))
 (8 4 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (7 7 (:REWRITE REDUCE-RATIONALP-+))
 (7 7 (:REWRITE REDUCE-RATIONALP-*))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE RATIONALP-MINUS-X))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal c (- x))|))
 (7 7 (:REWRITE |(equal (/ x) c)|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) c)|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 (7 7 (:META META-RATIONALP-CORRECT))
 (6 6 (:REWRITE THE-FLOOR-BELOW))
 (6 6 (:REWRITE THE-FLOOR-ABOVE))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (6 6 (:REWRITE SIMPLIFY-SUMS-<))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (6 6 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (6 6 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (6 6 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (6 6 (:REWRITE INTEGERP-<-CONSTANT))
 (6 6 (:REWRITE DEFAULT-LESS-THAN-2))
 (6 6 (:REWRITE DEFAULT-LESS-THAN-1))
 (6 6 (:REWRITE CONSTANT-<-INTEGERP))
 (6 6 (:REWRITE |(< y (+ (- c) x))|))
 (6 6 (:REWRITE |(< x (+ c/d y))|))
 (6 6 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (6 6 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (6 6 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (6 6 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (6 6 (:REWRITE |(< c (- x))|))
 (6 6 (:REWRITE |(< 0 (/ x))|))
 (6 6 (:REWRITE |(< 0 (* x y))|))
 (6 6 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (6 6 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (6 6 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (6 6 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (6 6 (:REWRITE |(< (/ x) (/ y))|))
 (6 6 (:REWRITE |(< (- x) c)|))
 (6 6 (:REWRITE |(< (- x) (- y))|))
 (4 2 (:REWRITE DM::INT-CADR-TRIPP))
 )
(DM::CONSP-NTHCDR
 (96 48 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (48 48 (:TYPE-PRESCRIPTION DM::ECP))
 (18 12 (:REWRITE DEFAULT-PLUS-2))
 (16 10 (:REWRITE DEFAULT-LESS-THAN-2))
 (14 10 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (14 8 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (13 8 (:REWRITE SIMPLIFY-SUMS-<))
 (12 12 (:REWRITE DEFAULT-PLUS-1))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE INTEGERP-<-CONSTANT))
 (10 10 (:REWRITE DEFAULT-LESS-THAN-1))
 (10 10 (:REWRITE CONSTANT-<-INTEGERP))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (10 10 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< c (- x))|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (10 10 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (10 10 (:REWRITE |(< (/ x) (/ y))|))
 (10 10 (:REWRITE |(< (- x) c)|))
 (10 10 (:REWRITE |(< (- x) (- y))|))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (9 9 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE ZP-OPEN))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:REWRITE |(< x (if a b c))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(DM::MEMBER-LEN-POS
 (144 72 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (144 72 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (72 72 (:TYPE-PRESCRIPTION DM::TRIPP))
 (72 72 (:TYPE-PRESCRIPTION DM::ECP))
 (46 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (40 8 (:REWRITE ACL2-NUMBERP-X))
 (16 4 (:REWRITE RATIONALP-X))
 (11 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (11 6 (:REWRITE DEFAULT-PLUS-2))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal c (- x))|))
 (7 7 (:REWRITE |(equal (/ x) c)|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) c)|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:REWRITE DEFAULT-PLUS-1))
 (5 5 (:REWRITE DM::PERM-MEMBER))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (4 4 (:META META-RATIONALP-CORRECT))
 (4 4 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 )
(DM::VARS)
(DM::VALS)
(DM::VLIST)
(DM::ALL-INTEGERS-VALS
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 )
(DM::LEN-VALS
 (10 5 (:REWRITE DEFAULT-PLUS-2))
 (6 6 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE NORMALIZE-ADDENDS))
 (5 5 (:REWRITE DEFAULT-PLUS-1))
 )
(DM::EVALP$)
(DM::EVALH$)
(DM::THETA)
(DM::SHNFP-THETA)
(DM::EVALH-THETA-0
 (244 30 (:REWRITE DEFAULT-PLUS-2))
 (224 30 (:REWRITE DEFAULT-PLUS-1))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (95 18 (:REWRITE DEFAULT-TIMES-2))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (54 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (53 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (34 18 (:REWRITE DEFAULT-TIMES-1))
 (15 8 (:REWRITE DEFAULT-EXPT-1))
 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (12 12 (:REWRITE NORMALIZE-ADDENDS))
 (8 8 (:REWRITE DEFAULT-EXPT-2))
 (8 8 (:REWRITE |(expt 1/c n)|))
 (8 8 (:REWRITE |(expt (- x) n)|))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE |(+ c (+ d x))|))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(DM::EVALH-THETA-1
 (244 30 (:REWRITE DEFAULT-PLUS-2))
 (224 30 (:REWRITE DEFAULT-PLUS-1))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (95 18 (:REWRITE DEFAULT-TIMES-2))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (54 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (53 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (34 18 (:REWRITE DEFAULT-TIMES-1))
 (15 8 (:REWRITE DEFAULT-EXPT-1))
 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (12 12 (:REWRITE NORMALIZE-ADDENDS))
 (8 8 (:REWRITE DEFAULT-EXPT-2))
 (8 8 (:REWRITE |(expt 1/c n)|))
 (8 8 (:REWRITE |(expt (- x) n)|))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE |(+ c (+ d x))|))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(DM::EVALH-THETA-2
 (244 30 (:REWRITE DEFAULT-PLUS-2))
 (224 30 (:REWRITE DEFAULT-PLUS-1))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (100 100 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (95 18 (:REWRITE DEFAULT-TIMES-2))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (54 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (53 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (34 18 (:REWRITE DEFAULT-TIMES-1))
 (15 8 (:REWRITE DEFAULT-EXPT-1))
 (12 12 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (12 12 (:REWRITE NORMALIZE-ADDENDS))
 (8 8 (:REWRITE DEFAULT-EXPT-2))
 (8 8 (:REWRITE |(expt 1/c n)|))
 (8 8 (:REWRITE |(expt (- x) n)|))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE |(+ c (+ d x))|))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (2 2 (:REWRITE |(equal c (/ x))|))
 (2 2 (:REWRITE |(equal c (- x))|))
 (2 2 (:REWRITE |(equal (/ x) c)|))
 (2 2 (:REWRITE |(equal (/ x) (/ y))|))
 (2 2 (:REWRITE |(equal (- x) c)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 )
(DM::ECP-MOD
 (42410 21205 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (42319 3 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (39509 15 (:LINEAR MOD-BOUNDS-1))
 (38605 537 (:REWRITE DEFAULT-PLUS-2))
 (24406 537 (:REWRITE DEFAULT-PLUS-1))
 (22095 162 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (21648 21205 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (21483 21483 (:TYPE-PRESCRIPTION DM::TRIPP))
 (16341 7 (:LINEAR RTL::MOD-BND-2))
 (16163 8515 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (15603 31 (:REWRITE RTL::MOD-DOES-NOTHING))
 (14777 31 (:REWRITE MOD-ZERO . 3))
 (13734 3 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (13232 16 (:LINEAR MOD-BOUNDS-2))
 (12875 4299 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (12875 4299 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (12539 31 (:REWRITE MOD-X-Y-=-X . 3))
 (12339 8515 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (12339 8515 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (12339 8515 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (12339 8515 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (12339 8515 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (12154 894 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (12154 894 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (12154 894 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (12112 31 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (11602 171 (:REWRITE RATIONALP-X))
 (11598 31 (:REWRITE MOD-X-Y-=-X . 4))
 (11009 31 (:REWRITE MOD-ZERO . 4))
 (8515 8515 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (8515 8515 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (7740 8 (:LINEAR MOD-BOUNDS-3))
 (6993 31 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (6289 161 (:REWRITE ACL2-NUMBERP-X))
 (6155 791 (:REWRITE DEFAULT-TIMES-1))
 (6013 31 (:REWRITE MOD-X-Y-=-X . 2))
 (5251 31 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (5251 31 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (5068 528 (:REWRITE DEFAULT-LESS-THAN-1))
 (4793 31 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (4709 31 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (4709 31 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (4277 552 (:REWRITE DEFAULT-LESS-THAN-2))
 (3777 512 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3137 335 (:META META-INTEGERP-CORRECT))
 (2163 2163 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (2163 2163 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (2163 2163 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (2103 512 (:REWRITE SIMPLIFY-SUMS-<))
 (1806 170 (:LINEAR EXPT->=-1-TWO))
 (1806 170 (:LINEAR EXPT->-1-TWO))
 (1806 170 (:LINEAR EXPT-<-1-ONE))
 (1712 170 (:LINEAR EXPT-<=-1-ONE))
 (1696 170 (:LINEAR EXPT-X->=-X))
 (1696 170 (:LINEAR EXPT->=-1-ONE))
 (1696 170 (:LINEAR EXPT-<=-1-TWO))
 (1654 170 (:LINEAR EXPT-X->-X))
 (1654 170 (:LINEAR EXPT->-1-ONE))
 (1654 170 (:LINEAR EXPT-<-1-TWO))
 (1636 157 (:REWRITE DM::INTEGERP-EC-X))
 (1415 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1312 26 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (1294 121 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1294 121 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1110 121 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1110 121 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (1043 336 (:REWRITE INTEGERP-MINUS-X))
 (943 33 (:REWRITE DEFAULT-MOD-1))
 (911 911 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (911 911 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (911 911 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (810 121 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (810 121 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (810 121 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (810 121 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (810 121 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (781 46 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (735 46 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (735 46 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (735 46 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (735 46 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (614 26 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (614 26 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (604 500 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (586 586 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (552 552 (:REWRITE THE-FLOOR-BELOW))
 (552 552 (:REWRITE THE-FLOOR-ABOVE))
 (535 31 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (535 31 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (535 31 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (513 512 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (513 512 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (512 512 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (512 512 (:REWRITE INTEGERP-<-CONSTANT))
 (512 512 (:REWRITE CONSTANT-<-INTEGERP))
 (512 512 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (512 512 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (512 512 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (512 512 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (512 512 (:REWRITE |(< c (- x))|))
 (512 512 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (512 512 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (512 512 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (512 512 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (512 512 (:REWRITE |(< (/ x) (/ y))|))
 (512 512 (:REWRITE |(< (- x) c)|))
 (512 512 (:REWRITE |(< (- x) (- y))|))
 (495 5 (:REWRITE |(- (+ x y))|))
 (435 157 (:REWRITE DM::INT-CAR-TRIPP))
 (363 161 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (340 340 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (340 340 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (340 340 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (340 340 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (335 335 (:REWRITE REDUCE-INTEGERP-+))
 (326 287 (:REWRITE NORMALIZE-ADDENDS))
 (295 13 (:REWRITE DEFAULT-MINUS))
 (286 286 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (222 222 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (171 171 (:REWRITE REDUCE-RATIONALP-+))
 (171 171 (:REWRITE REDUCE-RATIONALP-*))
 (171 171 (:REWRITE RATIONALP-MINUS-X))
 (171 171 (:META META-RATIONALP-CORRECT))
 (170 170 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (170 170 (:LINEAR EXPT-LINEAR-UPPER-<))
 (170 170 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (170 170 (:LINEAR EXPT-LINEAR-LOWER-<))
 (167 166 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (166 166 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (166 166 (:REWRITE |(equal c (/ x))|))
 (166 166 (:REWRITE |(equal c (- x))|))
 (166 166 (:REWRITE |(equal (/ x) c)|))
 (166 166 (:REWRITE |(equal (/ x) (/ y))|))
 (166 166 (:REWRITE |(equal (- x) c)|))
 (166 166 (:REWRITE |(equal (- x) (- y))|))
 (162 162 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (150 108 (:REWRITE DEFAULT-DIVIDE))
 (145 145 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (145 145 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (145 145 (:REWRITE |(< 0 (/ x))|))
 (145 145 (:REWRITE |(< 0 (* x y))|))
 (124 4 (:REWRITE |(equal (expt x n) 0)|))
 (108 108 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (101 101 (:REWRITE |(+ c (+ d x))|))
 (100 100 (:REWRITE FOLD-CONSTS-IN-+))
 (99 99 (:REWRITE |(* c (* d x))|))
 (90 2 (:REWRITE |(* (* x y) z)|))
 (82 82 (:REWRITE |(< (+ c/d x) y)|))
 (82 82 (:REWRITE |(< (+ (- c) x) y)|))
 (53 3 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (46 46 (:TYPE-PRESCRIPTION NATP))
 (46 1 (:REWRITE |(integerp (- x))|))
 (42 5 (:REWRITE |(- (* c x))|))
 (37 37 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (37 33 (:REWRITE DEFAULT-MOD-2))
 (32 32 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (31 31 (:REWRITE INTEGERP-/))
 (31 31 (:REWRITE |(mod x (- y))| . 3))
 (31 31 (:REWRITE |(mod x (- y))| . 2))
 (31 31 (:REWRITE |(mod x (- y))| . 1))
 (29 29 (:REWRITE |(equal (+ (- c) x) y)|))
 (26 26 (:REWRITE |(< y (+ (- c) x))|))
 (26 26 (:REWRITE |(< x (+ c/d y))|))
 (25 1 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (20 2 (:REWRITE |(- (- x))|))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (12 12 (:REWRITE |(< (/ x) 0)|))
 (12 12 (:REWRITE |(< (* x y) 0)|))
 (7 7 (:REWRITE DEFAULT-CAR))
 (7 7 (:LINEAR RTL::MOD-BND-3))
 (6 6 (:REWRITE DEFAULT-EXPT-2))
 (6 6 (:REWRITE DEFAULT-EXPT-1))
 (6 6 (:REWRITE |(expt 1/c n)|))
 (6 6 (:REWRITE |(expt (- x) n)|))
 (4 1 (:REWRITE DM::INTEGERP-EC-Y))
 (3 3 (:TYPE-PRESCRIPTION ABS))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 2 (:DEFINITION FIX))
 (1 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (1 1 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(DM::THETA-0-MOD
 (28418 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (21001 15 (:LINEAR MOD-BOUNDS-1))
 (15474 48 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (11373 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (6154 435 (:REWRITE DEFAULT-TIMES-2))
 (5469 28 (:REWRITE RTL::MOD-DOES-NOTHING))
 (5429 7 (:LINEAR RTL::MOD-BND-2))
 (4642 28 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4158 28 (:REWRITE MOD-ZERO . 3))
 (4000 435 (:REWRITE DEFAULT-TIMES-1))
 (3214 8 (:LINEAR MOD-BOUNDS-3))
 (3150 134 (:REWRITE DEFAULT-PLUS-2))
 (2824 28 (:REWRITE MOD-X-Y-=-X . 3))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2495 2495 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2347 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (2233 28 (:REWRITE MOD-X-Y-=-X . 4))
 (2223 28 (:REWRITE MOD-ZERO . 4))
 (1847 188 (:META META-INTEGERP-CORRECT))
 (1820 291 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1636 295 (:REWRITE DEFAULT-LESS-THAN-1))
 (1619 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1569 28 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1333 134 (:REWRITE DEFAULT-PLUS-1))
 (1238 291 (:REWRITE SIMPLIFY-SUMS-<))
 (1232 16 (:LINEAR MOD-BOUNDS-2))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1198 238 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1198 238 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1018 238 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1018 238 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (999 189 (:REWRITE INTEGERP-MINUS-X))
 (989 84 (:LINEAR EXPT-<=-1-ONE))
 (972 36 (:REWRITE REDUCE-RATIONALP-*))
 (930 31 (:REWRITE DEFAULT-MOD-1))
 (894 84 (:LINEAR EXPT-X->=-X))
 (888 84 (:LINEAR EXPT->=-1-TWO))
 (863 84 (:LINEAR EXPT->-1-TWO))
 (863 84 (:LINEAR EXPT-<-1-ONE))
 (861 28 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (861 28 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (849 84 (:LINEAR EXPT->=-1-ONE))
 (799 84 (:LINEAR EXPT-X->-X))
 (799 84 (:LINEAR EXPT->-1-ONE))
 (799 84 (:LINEAR EXPT-<-1-TWO))
 (797 84 (:LINEAR EXPT-<=-1-TWO))
 (695 295 (:REWRITE DEFAULT-LESS-THAN-2))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (623 28 (:REWRITE MOD-X-Y-=-X . 2))
 (616 28 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (616 28 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (616 28 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (601 46 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (559 5 (:REWRITE |(- (+ x y))|))
 (477 28 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (477 28 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (477 28 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (443 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (414 414 (:REWRITE DEFAULT-CDR))
 (411 411 (:REWRITE DEFAULT-CAR))
 (340 14 (:REWRITE DEFAULT-MINUS))
 (316 8 (:DEFINITION RFIX))
 (295 295 (:REWRITE THE-FLOOR-BELOW))
 (295 295 (:REWRITE THE-FLOOR-ABOVE))
 (292 291 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (292 291 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (291 291 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (291 291 (:REWRITE INTEGERP-<-CONSTANT))
 (291 291 (:REWRITE CONSTANT-<-INTEGERP))
 (291 291 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (291 291 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (291 291 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (291 291 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (291 291 (:REWRITE |(< c (- x))|))
 (291 291 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (291 291 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (291 291 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (291 291 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (291 291 (:REWRITE |(< (/ x) (/ y))|))
 (291 291 (:REWRITE |(< (- x) c)|))
 (291 291 (:REWRITE |(< (- x) (- y))|))
 (267 1 (:REWRITE |(* (if a b c) x)|))
 (246 238 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (246 238 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (246 238 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (246 238 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (246 238 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (246 238 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (246 238 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (196 106 (:REWRITE NORMALIZE-ADDENDS))
 (188 188 (:REWRITE REDUCE-INTEGERP-+))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (168 168 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (168 168 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (168 168 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (168 168 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (160 80 (:REWRITE DEFAULT-DIVIDE))
 (158 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (135 3 (:REWRITE |(* (* x y) z)|))
 (130 130 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (104 104 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (86 86 (:REWRITE |(< 0 (/ x))|))
 (86 86 (:REWRITE |(< 0 (* x y))|))
 (84 84 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (84 84 (:LINEAR EXPT-LINEAR-UPPER-<))
 (84 84 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (84 84 (:LINEAR EXPT-LINEAR-LOWER-<))
 (80 80 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (78 2 (:REWRITE |(equal (expt x n) 0)|))
 (76 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (62 31 (:REWRITE DEFAULT-MOD-2))
 (58 50 (:REWRITE |(equal (/ x) c)|))
 (58 50 (:REWRITE |(equal (/ x) (/ y))|))
 (54 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (53 45 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (53 45 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (52 50 (:REWRITE |(equal (- x) (- y))|))
 (52 1 (:REWRITE |(integerp (- x))|))
 (51 50 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE |(equal c (/ x))|))
 (50 50 (:REWRITE |(equal c (- x))|))
 (50 50 (:REWRITE |(equal (- x) c)|))
 (50 50 (:REWRITE |(+ c (+ d x))|))
 (48 48 (:REWRITE FOLD-CONSTS-IN-+))
 (48 48 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (46 5 (:REWRITE |(- (* c x))|))
 (45 45 (:TYPE-PRESCRIPTION NATP))
 (44 44 (:REWRITE |(* c (* d x))|))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (36 36 (:REWRITE REDUCE-RATIONALP-+))
 (36 36 (:REWRITE RATIONALP-MINUS-X))
 (36 36 (:META META-RATIONALP-CORRECT))
 (29 29 (:REWRITE |(< (+ c/d x) y)|))
 (29 29 (:REWRITE |(< (+ (- c) x) y)|))
 (28 28 (:REWRITE |(mod x (- y))| . 3))
 (28 28 (:REWRITE |(mod x (- y))| . 2))
 (28 28 (:REWRITE |(mod x (- y))| . 1))
 (27 18 (:REWRITE DEFAULT-EXPT-1))
 (24 8 (:REWRITE |(equal x (/ y))|))
 (24 2 (:REWRITE |(- (- x))|))
 (23 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (18 18 (:REWRITE DEFAULT-EXPT-2))
 (18 18 (:REWRITE |(expt 1/c n)|))
 (18 18 (:REWRITE |(expt (- x) n)|))
 (16 16 (:REWRITE INTEGERP-/))
 (16 16 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (16 8 (:REWRITE |(not (equal x (/ y)))|))
 (15 15 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (12 12 (:REWRITE |(equal (+ (- c) x) y)|))
 (10 5 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (7 7 (:REWRITE |(< y (+ (- c) x))|))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (7 7 (:LINEAR RTL::MOD-BND-3))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(DM::THETA-1-MOD
 (28418 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (20905 15 (:LINEAR MOD-BOUNDS-1))
 (15426 48 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (11373 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (5890 435 (:REWRITE DEFAULT-TIMES-2))
 (5397 28 (:REWRITE RTL::MOD-DOES-NOTHING))
 (5381 7 (:LINEAR RTL::MOD-BND-2))
 (4642 28 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4158 28 (:REWRITE MOD-ZERO . 3))
 (3736 435 (:REWRITE DEFAULT-TIMES-1))
 (3166 8 (:LINEAR MOD-BOUNDS-3))
 (3150 134 (:REWRITE DEFAULT-PLUS-2))
 (2824 28 (:REWRITE MOD-X-Y-=-X . 3))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2495 2495 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2347 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (2233 28 (:REWRITE MOD-X-Y-=-X . 4))
 (2223 28 (:REWRITE MOD-ZERO . 4))
 (1847 188 (:META META-INTEGERP-CORRECT))
 (1772 291 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1619 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1588 295 (:REWRITE DEFAULT-LESS-THAN-1))
 (1569 28 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1333 134 (:REWRITE DEFAULT-PLUS-1))
 (1214 291 (:REWRITE SIMPLIFY-SUMS-<))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1198 238 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1198 238 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1136 16 (:LINEAR MOD-BOUNDS-2))
 (1018 238 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1018 238 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (999 189 (:REWRITE INTEGERP-MINUS-X))
 (989 84 (:LINEAR EXPT-<=-1-ONE))
 (894 84 (:LINEAR EXPT-X->=-X))
 (888 84 (:LINEAR EXPT->=-1-TWO))
 (882 31 (:REWRITE DEFAULT-MOD-1))
 (876 36 (:REWRITE REDUCE-RATIONALP-*))
 (863 84 (:LINEAR EXPT->-1-TWO))
 (863 84 (:LINEAR EXPT-<-1-ONE))
 (861 28 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (861 28 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (849 84 (:LINEAR EXPT->=-1-ONE))
 (799 84 (:LINEAR EXPT-X->-X))
 (799 84 (:LINEAR EXPT->-1-ONE))
 (799 84 (:LINEAR EXPT-<-1-TWO))
 (797 84 (:LINEAR EXPT-<=-1-TWO))
 (695 295 (:REWRITE DEFAULT-LESS-THAN-2))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (623 28 (:REWRITE MOD-X-Y-=-X . 2))
 (616 28 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (616 28 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (616 28 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (601 46 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (559 5 (:REWRITE |(- (+ x y))|))
 (443 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (429 28 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (429 28 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (429 28 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (346 346 (:REWRITE DEFAULT-CDR))
 (343 343 (:REWRITE DEFAULT-CAR))
 (340 14 (:REWRITE DEFAULT-MINUS))
 (295 295 (:REWRITE THE-FLOOR-BELOW))
 (295 295 (:REWRITE THE-FLOOR-ABOVE))
 (292 291 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (292 291 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (291 291 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (291 291 (:REWRITE INTEGERP-<-CONSTANT))
 (291 291 (:REWRITE CONSTANT-<-INTEGERP))
 (291 291 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (291 291 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (291 291 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (291 291 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (291 291 (:REWRITE |(< c (- x))|))
 (291 291 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (291 291 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (291 291 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (291 291 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (291 291 (:REWRITE |(< (/ x) (/ y))|))
 (291 291 (:REWRITE |(< (- x) c)|))
 (291 291 (:REWRITE |(< (- x) (- y))|))
 (268 8 (:DEFINITION RFIX))
 (267 1 (:REWRITE |(* (if a b c) x)|))
 (246 238 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (246 238 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (246 238 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (246 238 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (246 238 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (246 238 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (246 238 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (196 106 (:REWRITE NORMALIZE-ADDENDS))
 (188 188 (:REWRITE REDUCE-INTEGERP-+))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (168 168 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (168 168 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (168 168 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (168 168 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (160 80 (:REWRITE DEFAULT-DIVIDE))
 (158 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (135 3 (:REWRITE |(* (* x y) z)|))
 (130 130 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (104 104 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (86 86 (:REWRITE |(< 0 (/ x))|))
 (86 86 (:REWRITE |(< 0 (* x y))|))
 (84 84 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (84 84 (:LINEAR EXPT-LINEAR-UPPER-<))
 (84 84 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (84 84 (:LINEAR EXPT-LINEAR-LOWER-<))
 (80 80 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (78 2 (:REWRITE |(equal (expt x n) 0)|))
 (76 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (62 31 (:REWRITE DEFAULT-MOD-2))
 (58 50 (:REWRITE |(equal (/ x) c)|))
 (58 50 (:REWRITE |(equal (/ x) (/ y))|))
 (54 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (53 45 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (53 45 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (52 50 (:REWRITE |(equal (- x) (- y))|))
 (52 1 (:REWRITE |(integerp (- x))|))
 (51 50 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE |(equal c (/ x))|))
 (50 50 (:REWRITE |(equal c (- x))|))
 (50 50 (:REWRITE |(equal (- x) c)|))
 (50 50 (:REWRITE |(+ c (+ d x))|))
 (48 48 (:REWRITE FOLD-CONSTS-IN-+))
 (48 48 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (46 5 (:REWRITE |(- (* c x))|))
 (45 45 (:TYPE-PRESCRIPTION NATP))
 (44 44 (:REWRITE |(* c (* d x))|))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (36 36 (:REWRITE REDUCE-RATIONALP-+))
 (36 36 (:REWRITE RATIONALP-MINUS-X))
 (36 36 (:META META-RATIONALP-CORRECT))
 (29 29 (:REWRITE |(< (+ c/d x) y)|))
 (29 29 (:REWRITE |(< (+ (- c) x) y)|))
 (28 28 (:REWRITE |(mod x (- y))| . 3))
 (28 28 (:REWRITE |(mod x (- y))| . 2))
 (28 28 (:REWRITE |(mod x (- y))| . 1))
 (27 18 (:REWRITE DEFAULT-EXPT-1))
 (24 8 (:REWRITE |(equal x (/ y))|))
 (24 2 (:REWRITE |(- (- x))|))
 (23 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (18 18 (:REWRITE DEFAULT-EXPT-2))
 (18 18 (:REWRITE |(expt 1/c n)|))
 (18 18 (:REWRITE |(expt (- x) n)|))
 (16 16 (:REWRITE INTEGERP-/))
 (16 16 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (16 8 (:REWRITE |(not (equal x (/ y)))|))
 (15 15 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (12 12 (:REWRITE |(equal (+ (- c) x) y)|))
 (10 5 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (7 7 (:REWRITE |(< y (+ (- c) x))|))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (7 7 (:LINEAR RTL::MOD-BND-3))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(DM::THETA-2-MOD
 (28418 4 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (20809 15 (:LINEAR MOD-BOUNDS-1))
 (15378 48 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (11373 4 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (5626 435 (:REWRITE DEFAULT-TIMES-2))
 (5333 7 (:LINEAR RTL::MOD-BND-2))
 (5325 28 (:REWRITE RTL::MOD-DOES-NOTHING))
 (4642 28 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (4158 28 (:REWRITE MOD-ZERO . 3))
 (3472 435 (:REWRITE DEFAULT-TIMES-1))
 (3150 134 (:REWRITE DEFAULT-PLUS-2))
 (3118 8 (:LINEAR MOD-BOUNDS-3))
 (2824 28 (:REWRITE MOD-X-Y-=-X . 3))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2669 2669 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (2495 2495 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2347 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-4D))
 (2233 28 (:REWRITE MOD-X-Y-=-X . 4))
 (2223 28 (:REWRITE MOD-ZERO . 4))
 (1847 188 (:META META-INTEGERP-CORRECT))
 (1724 291 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1619 1 (:REWRITE |(equal (mod a n) (mod b n))|))
 (1569 28 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1540 295 (:REWRITE DEFAULT-LESS-THAN-1))
 (1333 134 (:REWRITE DEFAULT-PLUS-1))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (1208 1208 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (1198 238 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (1198 238 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (1190 291 (:REWRITE SIMPLIFY-SUMS-<))
 (1040 16 (:LINEAR MOD-BOUNDS-2))
 (1018 238 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (1018 238 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (999 189 (:REWRITE INTEGERP-MINUS-X))
 (989 84 (:LINEAR EXPT-<=-1-ONE))
 (894 84 (:LINEAR EXPT-X->=-X))
 (888 84 (:LINEAR EXPT->=-1-TWO))
 (863 84 (:LINEAR EXPT->-1-TWO))
 (863 84 (:LINEAR EXPT-<-1-ONE))
 (861 28 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (861 28 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (849 84 (:LINEAR EXPT->=-1-ONE))
 (834 31 (:REWRITE DEFAULT-MOD-1))
 (799 84 (:LINEAR EXPT-X->-X))
 (799 84 (:LINEAR EXPT->-1-ONE))
 (799 84 (:LINEAR EXPT-<-1-TWO))
 (797 84 (:LINEAR EXPT-<=-1-TWO))
 (780 36 (:REWRITE REDUCE-RATIONALP-*))
 (695 295 (:REWRITE DEFAULT-LESS-THAN-2))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (634 634 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (623 28 (:REWRITE MOD-X-Y-=-X . 2))
 (616 28 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (616 28 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (616 28 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (601 46 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (559 5 (:REWRITE |(- (+ x y))|))
 (443 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (381 28 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (381 28 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (381 28 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (340 14 (:REWRITE DEFAULT-MINUS))
 (295 295 (:REWRITE THE-FLOOR-BELOW))
 (295 295 (:REWRITE THE-FLOOR-ABOVE))
 (292 291 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (292 291 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (291 291 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (291 291 (:REWRITE INTEGERP-<-CONSTANT))
 (291 291 (:REWRITE CONSTANT-<-INTEGERP))
 (291 291 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (291 291 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (291 291 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (291 291 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (291 291 (:REWRITE |(< c (- x))|))
 (291 291 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (291 291 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (291 291 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (291 291 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (291 291 (:REWRITE |(< (/ x) (/ y))|))
 (291 291 (:REWRITE |(< (- x) c)|))
 (291 291 (:REWRITE |(< (- x) (- y))|))
 (278 278 (:REWRITE DEFAULT-CDR))
 (275 275 (:REWRITE DEFAULT-CAR))
 (267 1 (:REWRITE |(* (if a b c) x)|))
 (246 238 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (246 238 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (246 238 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (246 238 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (246 238 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (246 238 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (246 238 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (220 8 (:DEFINITION RFIX))
 (196 106 (:REWRITE NORMALIZE-ADDENDS))
 (188 188 (:REWRITE REDUCE-INTEGERP-+))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-3D))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-2D))
 (183 183 (:TYPE-PRESCRIPTION NOT-INTEGERP-1D))
 (168 168 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (168 168 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (168 168 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (168 168 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (160 80 (:REWRITE DEFAULT-DIVIDE))
 (158 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (135 3 (:REWRITE |(* (* x y) z)|))
 (130 130 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (104 104 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (86 86 (:REWRITE |(< 0 (/ x))|))
 (86 86 (:REWRITE |(< 0 (* x y))|))
 (84 84 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (84 84 (:LINEAR EXPT-LINEAR-UPPER-<))
 (84 84 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (84 84 (:LINEAR EXPT-LINEAR-LOWER-<))
 (80 80 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (78 2 (:REWRITE |(equal (expt x n) 0)|))
 (76 4 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (62 31 (:REWRITE DEFAULT-MOD-2))
 (58 50 (:REWRITE |(equal (/ x) c)|))
 (58 50 (:REWRITE |(equal (/ x) (/ y))|))
 (54 2 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (53 45 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (53 45 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (52 50 (:REWRITE |(equal (- x) (- y))|))
 (52 1 (:REWRITE |(integerp (- x))|))
 (51 50 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (50 50 (:REWRITE |(equal c (/ x))|))
 (50 50 (:REWRITE |(equal c (- x))|))
 (50 50 (:REWRITE |(equal (- x) c)|))
 (50 50 (:REWRITE |(+ c (+ d x))|))
 (48 48 (:REWRITE FOLD-CONSTS-IN-+))
 (48 48 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (46 5 (:REWRITE |(- (* c x))|))
 (45 45 (:TYPE-PRESCRIPTION NATP))
 (44 44 (:REWRITE |(* c (* d x))|))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (36 36 (:REWRITE REDUCE-RATIONALP-+))
 (36 36 (:REWRITE RATIONALP-MINUS-X))
 (36 36 (:META META-RATIONALP-CORRECT))
 (29 29 (:REWRITE |(< (+ c/d x) y)|))
 (29 29 (:REWRITE |(< (+ (- c) x) y)|))
 (28 28 (:REWRITE |(mod x (- y))| . 3))
 (28 28 (:REWRITE |(mod x (- y))| . 2))
 (28 28 (:REWRITE |(mod x (- y))| . 1))
 (27 18 (:REWRITE DEFAULT-EXPT-1))
 (24 8 (:REWRITE |(equal x (/ y))|))
 (24 2 (:REWRITE |(- (- x))|))
 (23 23 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (18 18 (:REWRITE DEFAULT-EXPT-2))
 (18 18 (:REWRITE |(expt 1/c n)|))
 (18 18 (:REWRITE |(expt (- x) n)|))
 (16 16 (:REWRITE INTEGERP-/))
 (16 16 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (16 8 (:REWRITE |(not (equal x (/ y)))|))
 (15 15 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (15 15 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (12 12 (:REWRITE |(equal (+ (- c) x) y)|))
 (10 5 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (7 7 (:REWRITE |(< y (+ (- c) x))|))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (7 7 (:LINEAR RTL::MOD-BND-3))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:TYPE-PRESCRIPTION ABS))
 (2 2 (:REWRITE |(+ x (- x))|))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 (1 1 (:REWRITE |(* (- x) y)|))
 )
(DM::SPLIT$
 (15254 7627 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (11600 232 (:DEFINITION INTEGER-ABS))
 (9413 9413 (:TYPE-PRESCRIPTION DM::ECP))
 (7724 1352 (:REWRITE DEFAULT-PLUS-2))
 (6000 1352 (:REWRITE DEFAULT-PLUS-1))
 (4060 116 (:REWRITE |(+ (if a b c) x)|))
 (3782 135 (:REWRITE RATIONALP-X))
 (3364 348 (:REWRITE |(+ y x)|))
 (3364 116 (:REWRITE NUMERATOR-NEGATIVE))
 (2924 2924 (:TYPE-PRESCRIPTION DM::TRIPP))
 (2664 1302 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (2664 1302 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (1546 479 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (1358 669 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (1352 32 (:LINEAR ACL2-COUNT-OF-CONSP-POSITIVE))
 (1160 116 (:DEFINITION LENGTH))
 (1069 349 (:REWRITE DEFAULT-CDR))
 (1044 1044 (:TYPE-PRESCRIPTION NUMERATOR-ZERO))
 (1044 1044 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 2))
 (1044 1044 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
 (1044 1044 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 2))
 (1044 1044 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
 (1034 194 (:REWRITE DEFAULT-CAR))
 (888 888 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (888 888 (:REWRITE NORMALIZE-ADDENDS))
 (812 232 (:REWRITE DEFAULT-MINUS))
 (812 116 (:DEFINITION LEN))
 (681 2 (:REWRITE DM::SHFP-POP-POW-ATOM))
 (667 2 (:DEFINITION DM::SHFP))
 (641 249 (:REWRITE SIMPLIFY-SUMS-<))
 (641 249 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (600 24 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (408 136 (:REWRITE DM::INTEGERP-EC-Y))
 (381 19 (:REWRITE ACL2-NUMBERP-X))
 (371 371 (:REWRITE THE-FLOOR-BELOW))
 (371 371 (:REWRITE THE-FLOOR-ABOVE))
 (365 365 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (365 365 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (365 365 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (365 365 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (365 365 (:REWRITE INTEGERP-<-CONSTANT))
 (365 365 (:REWRITE CONSTANT-<-INTEGERP))
 (365 365 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (365 365 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (365 365 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (365 365 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (365 365 (:REWRITE |(< c (- x))|))
 (365 365 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (365 365 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (365 365 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (365 365 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (365 365 (:REWRITE |(< (/ x) (/ y))|))
 (365 365 (:REWRITE |(< (- x) c)|))
 (365 365 (:REWRITE |(< (- x) (- y))|))
 (364 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (353 353 (:REWRITE |(< (/ x) 0)|))
 (353 353 (:REWRITE |(< (* x y) 0)|))
 (318 106 (:REWRITE DM::INTEGERP-EC-X))
 (318 106 (:REWRITE DM::INT-CAR-TRIPP))
 (256 256 (:REWRITE REDUCE-INTEGERP-+))
 (256 256 (:REWRITE INTEGERP-MINUS-X))
 (256 256 (:META META-INTEGERP-CORRECT))
 (252 252 (:REWRITE FOLD-CONSTS-IN-+))
 (252 252 (:REWRITE |(+ c (+ d x))|))
 (237 237 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (237 237 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (225 75 (:REWRITE DM::INT-CADR-TRIPP))
 (201 3 (:DEFINITION NATP))
 (168 56 (:REWRITE DM::INT-CADDR-TRIPP))
 (135 135 (:REWRITE REDUCE-RATIONALP-+))
 (135 135 (:REWRITE REDUCE-RATIONALP-*))
 (135 135 (:REWRITE RATIONALP-MINUS-X))
 (135 135 (:META META-RATIONALP-CORRECT))
 (116 116 (:TYPE-PRESCRIPTION LEN))
 (116 116 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (116 116 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (116 116 (:REWRITE DEFAULT-REALPART))
 (116 116 (:REWRITE DEFAULT-RATIONAL-NUMERATOR))
 (116 116 (:REWRITE DEFAULT-RATIONAL-DENOMINATOR))
 (116 116 (:REWRITE DEFAULT-IMAGPART))
 (116 116 (:REWRITE DEFAULT-COERCE-2))
 (116 116 (:REWRITE DEFAULT-COERCE-1))
 (82 7 (:REWRITE DM::SHNFP-SHFP))
 (47 7 (:REWRITE DM::SHNFP-INT))
 (21 21 (:TYPE-PRESCRIPTION DM::SHNFP))
 (21 21 (:TYPE-PRESCRIPTION DM::SHFP))
 (10 5 (:REWRITE DM::SHNFP-POW-P))
 (7 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal c (- x))|))
 (7 7 (:REWRITE |(equal (/ x) c)|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) c)|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 (6 6 (:TYPE-PRESCRIPTION DM::NORM-POP))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (4 4 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (4 2 (:REWRITE DM::SHNFP-POW-Q))
 (2 2 (:TYPE-PRESCRIPTION DM::NORM-POW))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (2 2 (:REWRITE DM::DISTINCT-SYMBOLS-ATOM))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 )
(DM::SPLIT$-CASE-5-1
 (1459 925 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (776 776 (:TYPE-PRESCRIPTION DM::ECP))
 (604 370 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (604 370 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (454 454 (:TYPE-PRESCRIPTION DM::TRIPP))
 (377 227 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (224 85 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (177 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (132 3 (:REWRITE ACL2-NUMBERP-X))
 (75 3 (:REWRITE RATIONALP-X))
 (34 34 (:REWRITE DEFAULT-CDR))
 (20 4 (:REWRITE DM::SHNFP-INT))
 (12 4 (:REWRITE DM::INTEGERP-EC-X))
 (12 4 (:REWRITE DM::INT-CAR-TRIPP))
 (10 10 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-INTEGERP-CORRECT))
 (6 2 (:REWRITE DM::INT-CADR-TRIPP))
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (- x))|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) (/ y))|))
 (4 4 (:REWRITE |(< (- x) c)|))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3 3 (:REWRITE REDUCE-RATIONALP-+))
 (3 3 (:REWRITE REDUCE-RATIONALP-*))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE RATIONALP-MINUS-X))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE |(equal c (/ x))|))
 (3 3 (:REWRITE |(equal c (- x))|))
 (3 3 (:REWRITE |(equal (/ x) c)|))
 (3 3 (:REWRITE |(equal (/ x) (/ y))|))
 (3 3 (:REWRITE |(equal (- x) c)|))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (3 3 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:META META-RATIONALP-CORRECT))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(DM::SPLIT$-CASE-5-2
 (1035 713 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (421 421 (:TYPE-PRESCRIPTION DM::ECP))
 (334 235 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (334 235 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (231 154 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (230 230 (:TYPE-PRESCRIPTION DM::TRIPP))
 (216 81 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 1 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(DM::SPLIT$-CASE-5-3
 (3010 1795 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (1647 1647 (:TYPE-PRESCRIPTION DM::ECP))
 (1001 589 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (1001 589 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (994 994 (:TYPE-PRESCRIPTION DM::TRIPP))
 (665 381 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (554 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (537 287 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (398 6 (:REWRITE ACL2-NUMBERP-X))
 (220 6 (:REWRITE RATIONALP-X))
 (195 15 (:REWRITE DM::SHNFP-INT))
 (64 40 (:REWRITE DEFAULT-CDR))
 (59 17 (:REWRITE DEFAULT-CAR))
 (30 10 (:REWRITE DM::INTEGERP-EC-X))
 (30 10 (:REWRITE DM::INT-CAR-TRIPP))
 (18 6 (:REWRITE DM::INT-CADR-TRIPP))
 (18 6 (:REWRITE DM::INT-CADDR-TRIPP))
 (13 13 (:REWRITE REDUCE-INTEGERP-+))
 (13 13 (:REWRITE INTEGERP-MINUS-X))
 (13 13 (:META META-INTEGERP-CORRECT))
 (7 7 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 7 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (7 7 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (7 7 (:REWRITE |(equal c (/ x))|))
 (7 7 (:REWRITE |(equal c (- x))|))
 (7 7 (:REWRITE |(equal (/ x) c)|))
 (7 7 (:REWRITE |(equal (/ x) (/ y))|))
 (7 7 (:REWRITE |(equal (- x) c)|))
 (7 7 (:REWRITE |(equal (- x) (- y))|))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:META META-RATIONALP-CORRECT))
 (6 2 (:REWRITE DM::CADDR-0-TRIPP-2))
 (3 3 (:REWRITE THE-FLOOR-BELOW))
 (3 3 (:REWRITE THE-FLOOR-ABOVE))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE SIMPLIFY-SUMS-<))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (3 3 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3 3 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 3 (:REWRITE INTEGERP-<-CONSTANT))
 (3 3 (:REWRITE DEFAULT-LESS-THAN-2))
 (3 3 (:REWRITE DEFAULT-LESS-THAN-1))
 (3 3 (:REWRITE CONSTANT-<-INTEGERP))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (3 3 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< c (- x))|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (3 3 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (3 3 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE |(< (/ x) (/ y))|))
 (3 3 (:REWRITE |(< (- x) c)|))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 )
(DM::NTHCDR-CDR
 (1472 632 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (633 633 (:TYPE-PRESCRIPTION DM::ECP))
 (290 6 (:REWRITE DM::CONSP-NTHCDR))
 (268 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (186 6 (:REWRITE ACL2-NUMBERP-X))
 (128 4 (:DEFINITION NATP))
 (90 3 (:REWRITE RATIONALP-X))
 (88 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (68 4 (:DEFINITION LEN))
 (40 8 (:REWRITE |(+ y x)|))
 (28 22 (:REWRITE DEFAULT-PLUS-2))
 (22 22 (:REWRITE DEFAULT-PLUS-1))
 (14 14 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (14 14 (:REWRITE NORMALIZE-ADDENDS))
 (12 6 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (12 6 (:REWRITE DEFAULT-LESS-THAN-2))
 (10 10 (:REWRITE ZP-OPEN))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-INTEGERP-CORRECT))
 (6 6 (:REWRITE THE-FLOOR-BELOW))
 (6 6 (:REWRITE THE-FLOOR-ABOVE))
 (6 6 (:REWRITE SIMPLIFY-SUMS-<))
 (6 6 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (6 6 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (6 6 (:REWRITE INTEGERP-<-CONSTANT))
 (6 6 (:REWRITE DEFAULT-LESS-THAN-1))
 (6 6 (:REWRITE CONSTANT-<-INTEGERP))
 (6 6 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (6 6 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (6 6 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (6 6 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (6 6 (:REWRITE |(< c (- x))|))
 (6 6 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (6 6 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (6 6 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (6 6 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (6 6 (:REWRITE |(< (/ x) (/ y))|))
 (6 6 (:REWRITE |(< (- x) c)|))
 (6 6 (:REWRITE |(< (- x) (- y))|))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (5 5 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (5 5 (:REWRITE |(equal c (/ x))|))
 (5 5 (:REWRITE |(equal c (- x))|))
 (5 5 (:REWRITE |(equal (/ x) c)|))
 (5 5 (:REWRITE |(equal (/ x) (/ y))|))
 (5 5 (:REWRITE |(equal (- x) c)|))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE |(< (/ x) 0)|))
 (4 4 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:REWRITE REDUCE-RATIONALP-+))
 (3 3 (:REWRITE REDUCE-RATIONALP-*))
 (3 3 (:REWRITE RATIONALP-MINUS-X))
 (3 3 (:META META-RATIONALP-CORRECT))
 (2 2 (:REWRITE |(< x (if a b c))|))
 (2 2 (:REWRITE |(< (+ c/d x) y)|))
 (2 2 (:REWRITE |(< (+ (- c) x) y)|))
 (2 1 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (2 1 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (1 1 (:TYPE-PRESCRIPTION DM::TRIPP))
 )
(DM::CDR-NTHCDR
 (84 21 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (50 7 (:REWRITE DEFAULT-CDR))
 (38 1 (:REWRITE DM::CONSP-NTHCDR))
 (21 21 (:TYPE-PRESCRIPTION DM::ECP))
 (12 11 (:REWRITE DEFAULT-PLUS-2))
 (11 11 (:REWRITE DEFAULT-PLUS-1))
 (7 1 (:DEFINITION LEN))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE NORMALIZE-ADDENDS))
 (3 2 (:REWRITE SIMPLIFY-SUMS-<))
 (3 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (3 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(DM::CAR0
 (10 5 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (10 5 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (5 5 (:TYPE-PRESCRIPTION DM::TRIPP))
 (5 5 (:TYPE-PRESCRIPTION DM::ECP))
 )
(DM::EVALH-POW-REWRITE
 (412529 1127 (:REWRITE ACL2-NUMBERP-X))
 (399824 1103 (:REWRITE RATIONALP-X))
 (385963 710 (:REWRITE DM::INTEGERP-EVALH))
 (382425 724 (:DEFINITION DM::SHFP))
 (170250 1456 (:DEFINITION NATP))
 (148726 74363 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (107403 107403 (:TYPE-PRESCRIPTION DM::ECP))
 (63518 18870 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (62145 62145 (:TYPE-PRESCRIPTION DM::TRIPP))
 (58324 29162 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (58324 29162 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (37740 18870 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (28477 1870 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (24141 24141 (:TYPE-PRESCRIPTION DM::SHNFP))
 (24098 5522 (:REWRITE DEFAULT-CAR))
 (12694 6347 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (11472 1673 (:REWRITE DEFAULT-PLUS-1))
 (9724 107 (:DEFINITION NTHCDR))
 (8890 25 (:REWRITE DM::NTHCDR-CDR))
 (8598 8598 (:TYPE-PRESCRIPTION DM::SHFP))
 (7351 977 (:REWRITE DEFAULT-TIMES-1))
 (6816 2988 (:REWRITE DM::INTEGERP-EC-X))
 (6816 2988 (:REWRITE DM::INT-CAR-TRIPP))
 (6634 107 (:REWRITE ZP-OPEN))
 (5913 2687 (:REWRITE DM::INT-CADR-TRIPP))
 (5748 2874 (:REWRITE DM::SHNFP-SHFP))
 (5665 25 (:REWRITE DM::CONSP-NTHCDR))
 (5202 1456 (:REWRITE DM::SPLIT$-CASE-5-2))
 (4012 712 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4012 712 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (3803 3803 (:REWRITE REDUCE-INTEGERP-+))
 (3803 3803 (:REWRITE INTEGERP-MINUS-X))
 (3803 3803 (:META META-INTEGERP-CORRECT))
 (2040 50 (:REWRITE DM::SPLIT$-CASE-5-3))
 (2034 1870 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1870 1870 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1870 1870 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1870 1870 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1870 1870 (:REWRITE |(equal c (/ x))|))
 (1870 1870 (:REWRITE |(equal c (- x))|))
 (1870 1870 (:REWRITE |(equal (/ x) c)|))
 (1870 1870 (:REWRITE |(equal (/ x) (/ y))|))
 (1870 1870 (:REWRITE |(equal (- x) c)|))
 (1870 1870 (:REWRITE |(equal (- x) (- y))|))
 (1570 1570 (:REWRITE THE-FLOOR-BELOW))
 (1570 1570 (:REWRITE THE-FLOOR-ABOVE))
 (1570 1570 (:REWRITE SIMPLIFY-SUMS-<))
 (1570 1570 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1570 1570 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1570 1570 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1570 1570 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1570 1570 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1570 1570 (:REWRITE INTEGERP-<-CONSTANT))
 (1570 1570 (:REWRITE DEFAULT-LESS-THAN-2))
 (1570 1570 (:REWRITE DEFAULT-LESS-THAN-1))
 (1570 1570 (:REWRITE CONSTANT-<-INTEGERP))
 (1570 1570 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1570 1570 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1570 1570 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1570 1570 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1570 1570 (:REWRITE |(< c (- x))|))
 (1570 1570 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1570 1570 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1570 1570 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1570 1570 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1570 1570 (:REWRITE |(< (/ x) (/ y))|))
 (1570 1570 (:REWRITE |(< (- x) c)|))
 (1570 1570 (:REWRITE |(< (- x) (- y))|))
 (1463 1463 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1463 1463 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1463 1463 (:REWRITE |(< (/ x) 0)|))
 (1463 1463 (:REWRITE |(< (* x y) 0)|))
 (1424 712 (:REWRITE DM::INT-CADDR-TRIPP))
 (1258 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1103 1103 (:REWRITE REDUCE-RATIONALP-+))
 (1103 1103 (:REWRITE REDUCE-RATIONALP-*))
 (1103 1103 (:REWRITE RATIONALP-MINUS-X))
 (1103 1103 (:META META-RATIONALP-CORRECT))
 (1042 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1042 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1042 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (952 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (900 75 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (849 483 (:REWRITE DM::SHNFP-INT))
 (768 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (768 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (768 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (768 752 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (502 502 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (502 502 (:REWRITE NORMALIZE-ADDENDS))
 (179 179 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (174 174 (:REWRITE |(expt 1/c n)|))
 (174 174 (:REWRITE |(expt (- x) n)|))
 (107 107 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (107 107 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (107 107 (:REWRITE |(< 0 (/ x))|))
 (107 107 (:REWRITE |(< 0 (* x y))|))
 (100 25 (:REWRITE DM::SHNFP-POW-Q))
 (100 25 (:REWRITE DM::SHNFP-POW-P))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (80 80 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (75 75 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (75 25 (:REWRITE DM::INTEGERP-EC-Y))
 (68 68 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (50 50 (:REWRITE DM::P-NAT))
 (50 50 (:REWRITE DM::NATP-Y2))
 (50 50 (:REWRITE DM::NATP-Y1))
 (50 50 (:REWRITE DM::NATP-Y0))
 (50 50 (:REWRITE DM::NATP-X2))
 (50 50 (:REWRITE DM::NATP-X1))
 (50 50 (:REWRITE DM::NATP-X0))
 (50 50 (:REWRITE DM::NATP-P-1/2))
 (25 25 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(expt (if a b c) x)|))
 )
(DM::SPLIT$-CASE-5-4
 (14400 45 (:REWRITE ACL2-NUMBERP-X))
 (13902 42 (:REWRITE RATIONALP-X))
 (13327 25 (:REWRITE DM::INTEGERP-EVALH))
 (13205 31 (:DEFINITION DM::SHFP))
 (6524 3262 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (4957 4957 (:TYPE-PRESCRIPTION DM::ECP))
 (3964 76 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3142 1571 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (3142 1571 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (2995 2995 (:TYPE-PRESCRIPTION DM::TRIPP))
 (2472 996 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (2096 288 (:REWRITE DEFAULT-CAR))
 (2042 1117 (:REWRITE DEFAULT-CDR))
 (1992 996 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (1496 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1176 1176 (:TYPE-PRESCRIPTION DM::SHNFP))
 (976 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (896 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (896 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (896 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (563 414 (:REWRITE DEFAULT-PLUS-1))
 (444 270 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (444 270 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (436 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (436 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (436 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (436 406 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (357 357 (:TYPE-PRESCRIPTION DM::SHFP))
 (348 174 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (260 260 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (260 260 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (260 260 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (260 260 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (260 10 (:REWRITE DM::CONSP-NTHCDR))
 (242 121 (:REWRITE DM::SHNFP-SHFP))
 (229 105 (:REWRITE DM::INTEGERP-EC-X))
 (229 105 (:REWRITE DM::INT-CAR-TRIPP))
 (199 34 (:REWRITE DEFAULT-TIMES-1))
 (196 94 (:REWRITE DM::INT-CADR-TRIPP))
 (186 186 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (186 186 (:REWRITE NORMALIZE-ADDENDS))
 (154 14 (:DEFINITION NTH))
 (147 147 (:REWRITE REDUCE-INTEGERP-+))
 (147 147 (:REWRITE INTEGERP-MINUS-X))
 (147 147 (:META META-INTEGERP-CORRECT))
 (126 76 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (118 59 (:REWRITE DM::SPLIT$-CASE-5-2))
 (105 105 (:REWRITE ZP-OPEN))
 (85 85 (:REWRITE THE-FLOOR-BELOW))
 (85 85 (:REWRITE THE-FLOOR-ABOVE))
 (85 85 (:REWRITE SIMPLIFY-SUMS-<))
 (85 85 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (85 85 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (85 85 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (85 85 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (85 85 (:REWRITE INTEGERP-<-CONSTANT))
 (85 85 (:REWRITE DEFAULT-LESS-THAN-2))
 (85 85 (:REWRITE DEFAULT-LESS-THAN-1))
 (85 85 (:REWRITE CONSTANT-<-INTEGERP))
 (85 85 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (85 85 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (85 85 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (85 85 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (85 85 (:REWRITE |(< c (- x))|))
 (85 85 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (85 85 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (85 85 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (85 85 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (85 85 (:REWRITE |(< (/ x) (/ y))|))
 (85 85 (:REWRITE |(< (- x) c)|))
 (85 85 (:REWRITE |(< (- x) (- y))|))
 (76 76 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (76 76 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (76 76 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (76 76 (:REWRITE |(equal c (/ x))|))
 (76 76 (:REWRITE |(equal c (- x))|))
 (76 76 (:REWRITE |(equal (/ x) c)|))
 (76 76 (:REWRITE |(equal (/ x) (/ y))|))
 (76 76 (:REWRITE |(equal (- x) c)|))
 (76 76 (:REWRITE |(equal (- x) (- y))|))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (73 73 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (73 73 (:REWRITE |(< (/ x) 0)|))
 (73 73 (:REWRITE |(< (* x y) 0)|))
 (56 28 (:REWRITE DM::INT-CADDR-TRIPP))
 (56 2 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (42 42 (:REWRITE REDUCE-RATIONALP-+))
 (42 42 (:REWRITE REDUCE-RATIONALP-*))
 (42 42 (:REWRITE RATIONALP-MINUS-X))
 (42 42 (:META META-RATIONALP-CORRECT))
 (12 12 (:REWRITE DM::LEN-VALS))
 (10 10 (:REWRITE |(expt 1/c n)|))
 (10 10 (:REWRITE |(expt (- x) n)|))
 (5 5 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE DM::ALL-INTEGERS-VALS))
 (2 2 (:REWRITE |(expt (if a b c) x)|))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 )
(DM::SPLIT$-CASE-5-5
 (72 36 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (72 36 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (52 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (39 1 (:REWRITE ACL2-NUMBERP-X))
 (38 38 (:TYPE-PRESCRIPTION DM::TRIPP))
 (38 38 (:TYPE-PRESCRIPTION DM::ECP))
 (22 1 (:REWRITE RATIONALP-X))
 (11 1 (:DEFINITION NTHCDR))
 (11 1 (:DEFINITION NTH))
 (5 1 (:REWRITE |(+ y x)|))
 (4 2 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-PLUS-2))
 (3 3 (:REWRITE DEFAULT-PLUS-1))
 (3 2 (:REWRITE DEFAULT-CAR))
 (3 1 (:REWRITE DM::INTEGERP-EC-X))
 (3 1 (:REWRITE DM::INT-CAR-TRIPP))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE DM::SHNFP-INT))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(DM::SPLIT$-CASE-5-6
 (60 20 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (56 28 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (56 28 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (52 52 (:TYPE-PRESCRIPTION DM::ECP))
 (48 24 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (38 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (38 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (36 36 (:TYPE-PRESCRIPTION DM::TRIPP))
 (24 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (24 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (24 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (24 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (24 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (24 18 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (23 17 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (23 17 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (20 20 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS))
 (16 8 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (11 1 (:DEFINITION NTHCDR))
 (11 1 (:DEFINITION NTH))
 (5 1 (:REWRITE |(+ y x)|))
 (4 2 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-PLUS-2))
 (3 3 (:REWRITE DEFAULT-PLUS-1))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 1 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (2 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE THE-FLOOR-BELOW))
 (1 1 (:REWRITE THE-FLOOR-ABOVE))
 (1 1 (:REWRITE SIMPLIFY-SUMS-<))
 (1 1 (:REWRITE DM::SHNFP-INT))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1 1 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1 1 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE INTEGERP-<-CONSTANT))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-2))
 (1 1 (:REWRITE DEFAULT-LESS-THAN-1))
 (1 1 (:REWRITE CONSTANT-<-INTEGERP))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1 1 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< c (- x))|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1 1 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1 1 (:REWRITE |(< (/ x) (/ y))|))
 (1 1 (:REWRITE |(< (- x) c)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(DM::SPLIT$-CASE-5-7
 (5792 1 (:DEFINITION DM::EVALH))
 (4842 14 (:REWRITE ACL2-NUMBERP-X))
 (4574 14 (:REWRITE RATIONALP-X))
 (4200 8 (:DEFINITION DM::SHFP))
 (2616 24 (:REWRITE DEFAULT-PLUS-2))
 (2191 14 (:REWRITE DEFAULT-TIMES-2))
 (1742 871 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (1281 1281 (:TYPE-PRESCRIPTION DM::ECP))
 (940 366 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (794 794 (:TYPE-PRESCRIPTION DM::TRIPP))
 (776 233 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (732 366 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (614 22 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (603 1 (:REWRITE DM::EVALH-POW-REWRITE))
 (466 233 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (315 221 (:REWRITE DEFAULT-CDR))
 (290 61 (:REWRITE DEFAULT-CAR))
 (289 5 (:REWRITE DEFAULT-EXPT-2))
 (214 107 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (183 7 (:REWRITE |(+ (if a b c) x)|))
 (153 22 (:REWRITE DEFAULT-PLUS-1))
 (141 3 (:REWRITE DEFAULT-EXPT-1))
 (134 2 (:DEFINITION NTHCDR))
 (126 42 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (124 1 (:REWRITE DM::NTHCDR+))
 (98 12 (:REWRITE DEFAULT-TIMES-1))
 (98 5 (:REWRITE |(* (if a b c) x)|))
 (78 34 (:REWRITE DM::INTEGERP-EC-X))
 (78 34 (:REWRITE DM::INT-CAR-TRIPP))
 (66 30 (:REWRITE DM::INT-CADR-TRIPP))
 (64 3 (:REWRITE ZP-OPEN))
 (56 2 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (52 2 (:REWRITE DM::CONSP-NTHCDR))
 (46 46 (:REWRITE REDUCE-INTEGERP-+))
 (46 46 (:REWRITE INTEGERP-MINUS-X))
 (46 46 (:META META-INTEGERP-CORRECT))
 (36 9 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (36 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (35 17 (:REWRITE DM::SPLIT$-CASE-5-2))
 (35 3 (:REWRITE |(+ y x)|))
 (26 2 (:REWRITE ZIP-OPEN))
 (23 23 (:REWRITE THE-FLOOR-BELOW))
 (23 23 (:REWRITE THE-FLOOR-ABOVE))
 (23 23 (:REWRITE SIMPLIFY-SUMS-<))
 (23 23 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (23 23 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (23 23 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (23 23 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (23 23 (:REWRITE INTEGERP-<-CONSTANT))
 (23 23 (:REWRITE DEFAULT-LESS-THAN-2))
 (23 23 (:REWRITE DEFAULT-LESS-THAN-1))
 (23 23 (:REWRITE CONSTANT-<-INTEGERP))
 (23 23 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (23 23 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (23 23 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (23 23 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (23 23 (:REWRITE |(< c (- x))|))
 (23 23 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (23 23 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (23 23 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (23 23 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (23 23 (:REWRITE |(< (/ x) (/ y))|))
 (23 23 (:REWRITE |(< (- x) c)|))
 (23 23 (:REWRITE |(< (- x) (- y))|))
 (22 22 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (22 22 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (22 22 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (22 22 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (22 22 (:REWRITE |(equal c (/ x))|))
 (22 22 (:REWRITE |(equal c (- x))|))
 (22 22 (:REWRITE |(equal (/ x) c)|))
 (22 22 (:REWRITE |(equal (/ x) (/ y))|))
 (22 22 (:REWRITE |(equal (- x) c)|))
 (22 22 (:REWRITE |(equal (- x) (- y))|))
 (19 19 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (18 18 (:REWRITE |(< (/ x) 0)|))
 (18 18 (:REWRITE |(< (* x y) 0)|))
 (16 8 (:REWRITE DM::INT-CADDR-TRIPP))
 (14 14 (:REWRITE REDUCE-RATIONALP-+))
 (14 14 (:REWRITE REDUCE-RATIONALP-*))
 (14 14 (:REWRITE RATIONALP-MINUS-X))
 (14 14 (:META META-RATIONALP-CORRECT))
 (14 1 (:REWRITE |(expt 0 n)|))
 (12 1 (:REWRITE DM::CAR-NTHCDR))
 (11 1 (:DEFINITION NTH))
 (9 9 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (9 9 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (9 9 (:TYPE-PRESCRIPTION EXPT))
 (8 8 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (8 8 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DM::LEN-VALS))
 (4 4 (:REWRITE |(+ 0 x)|))
 (4 4 (:REWRITE |(* 1 x)|))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 (2 2 (:REWRITE |(* 0 x)|))
 (2 1 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-7))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE DM::SHNFP-INT))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(DM::SPLIT$-CASE-5-8
 (6639 1 (:DEFINITION DM::EVALH))
 (5514 30 (:REWRITE ACL2-NUMBERP-X))
 (4538 30 (:REWRITE RATIONALP-X))
 (4192 25 (:REWRITE DEFAULT-PLUS-2))
 (3438 6 (:DEFINITION DM::SHFP))
 (2294 1147 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (1516 1516 (:TYPE-PRESCRIPTION DM::ECP))
 (1342 23 (:REWRITE DEFAULT-PLUS-1))
 (1277 13 (:REWRITE DEFAULT-TIMES-2))
 (1022 329 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (951 1 (:REWRITE DM::EVALH-POW-REWRITE))
 (910 212 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (810 18 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (704 704 (:TYPE-PRESCRIPTION DM::TRIPP))
 (688 6 (:REWRITE |(+ (if a b c) x)|))
 (658 329 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (452 203 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-7))
 (424 212 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (378 126 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (338 49 (:REWRITE DEFAULT-CAR))
 (289 5 (:REWRITE DEFAULT-EXPT-2))
 (284 172 (:REWRITE DEFAULT-CDR))
 (264 5 (:REWRITE |(* (if a b c) x)|))
 (178 89 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (144 45 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (144 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (141 3 (:REWRITE DEFAULT-EXPT-1))
 (136 1 (:REWRITE DM::NTHCDR+))
 (134 2 (:DEFINITION NTHCDR))
 (98 12 (:REWRITE DEFAULT-TIMES-1))
 (66 28 (:REWRITE DM::INTEGERP-EC-X))
 (66 28 (:REWRITE DM::INT-CAR-TRIPP))
 (64 3 (:REWRITE ZP-OPEN))
 (56 2 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (54 24 (:REWRITE DM::INT-CADR-TRIPP))
 (52 2 (:REWRITE DM::CONSP-NTHCDR))
 (50 4 (:REWRITE |(* 1 x)|))
 (49 12 (:REWRITE DM::SPLIT$-CASE-5-7))
 (46 46 (:REWRITE REDUCE-INTEGERP-+))
 (46 46 (:REWRITE INTEGERP-MINUS-X))
 (46 46 (:META META-INTEGERP-CORRECT))
 (45 45 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (45 45 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (45 45 (:TYPE-PRESCRIPTION EXPT))
 (38 3 (:REWRITE |(+ y x)|))
 (27 13 (:REWRITE DM::SPLIT$-CASE-5-2))
 (26 2 (:REWRITE ZIP-OPEN))
 (19 19 (:REWRITE THE-FLOOR-BELOW))
 (19 19 (:REWRITE THE-FLOOR-ABOVE))
 (19 19 (:REWRITE SIMPLIFY-SUMS-<))
 (19 19 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (19 19 (:REWRITE REDUCE-RATIONALP-+))
 (19 19 (:REWRITE REDUCE-RATIONALP-*))
 (19 19 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (19 19 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (19 19 (:REWRITE RATIONALP-MINUS-X))
 (19 19 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (19 19 (:REWRITE INTEGERP-<-CONSTANT))
 (19 19 (:REWRITE DEFAULT-LESS-THAN-2))
 (19 19 (:REWRITE DEFAULT-LESS-THAN-1))
 (19 19 (:REWRITE CONSTANT-<-INTEGERP))
 (19 19 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (19 19 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (19 19 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (19 19 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (19 19 (:REWRITE |(< c (- x))|))
 (19 19 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (19 19 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (19 19 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (19 19 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (19 19 (:REWRITE |(< (/ x) (/ y))|))
 (19 19 (:REWRITE |(< (- x) c)|))
 (19 19 (:REWRITE |(< (- x) (- y))|))
 (19 19 (:META META-RATIONALP-CORRECT))
 (18 18 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (18 18 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (18 18 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (18 18 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (18 18 (:REWRITE |(equal c (/ x))|))
 (18 18 (:REWRITE |(equal c (- x))|))
 (18 18 (:REWRITE |(equal (/ x) c)|))
 (18 18 (:REWRITE |(equal (/ x) (/ y))|))
 (18 18 (:REWRITE |(equal (- x) c)|))
 (18 18 (:REWRITE |(equal (- x) (- y))|))
 (15 15 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (14 14 (:REWRITE |(< (/ x) 0)|))
 (14 14 (:REWRITE |(< (* x y) 0)|))
 (14 2 (:REWRITE DM::SHNFP-INT))
 (14 1 (:REWRITE |(expt 0 n)|))
 (12 6 (:REWRITE DM::INT-CADDR-TRIPP))
 (12 1 (:REWRITE DM::CAR-NTHCDR))
 (11 1 (:DEFINITION NTH))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (8 8 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DM::LEN-VALS))
 (3 3 (:REWRITE |(+ 0 x)|))
 (3 1 (:REWRITE DM::INTEGERP-EC-Y))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 (2 2 (:REWRITE |(* 0 x)|))
 (2 1 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-8))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(DM::SPLIT$-CASE-9
 (3652 1 (:DEFINITION DM::EVALH))
 (2808 14 (:REWRITE DEFAULT-PLUS-2))
 (2782 16 (:REWRITE ACL2-NUMBERP-X))
 (1977 16 (:REWRITE RATIONALP-X))
 (1143 13 (:REWRITE DEFAULT-PLUS-1))
 (1132 2 (:REWRITE DM::INTEGERP-EVALH))
 (1122 2 (:DEFINITION DM::SHFP))
 (998 499 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (912 304 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (768 768 (:TYPE-PRESCRIPTION DM::ECP))
 (702 247 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (603 1 (:REWRITE DM::EVALH-POW-REWRITE))
 (552 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (494 247 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (488 488 (:TYPE-PRESCRIPTION DM::TRIPP))
 (306 306 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS))
 (300 150 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (194 24 (:REWRITE DEFAULT-CAR))
 (154 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (154 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (148 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (148 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (148 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (148 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (148 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (148 58 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (147 4 (:REWRITE DEFAULT-TIMES-1))
 (140 56 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (140 56 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (140 56 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (138 1 (:REWRITE |(+ (if a b c) x)|))
 (125 1 (:REWRITE |(* (if a b c) x)|))
 (124 1 (:REWRITE DM::NTHCDR+))
 (122 68 (:REWRITE DEFAULT-CDR))
 (120 3 (:DEFINITION NTHCDR))
 (106 53 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (95 3 (:REWRITE DEFAULT-EXPT-2))
 (68 4 (:REWRITE |(+ y x)|))
 (66 5 (:REWRITE ZP-OPEN))
 (65 4 (:REWRITE DEFAULT-TIMES-2))
 (46 2 (:REWRITE DEFAULT-EXPT-1))
 (36 14 (:REWRITE DM::INTEGERP-EC-X))
 (36 14 (:REWRITE DM::INT-CAR-TRIPP))
 (24 24 (:TYPE-PRESCRIPTION DM::SHFP))
 (24 10 (:REWRITE DM::INT-CADR-TRIPP))
 (24 1 (:REWRITE |(* 1 x)|))
 (22 2 (:DEFINITION NTH))
 (20 20 (:REWRITE REDUCE-INTEGERP-+))
 (20 20 (:REWRITE INTEGERP-MINUS-X))
 (20 20 (:META META-INTEGERP-CORRECT))
 (16 8 (:REWRITE DM::SHNFP-SHFP))
 (15 5 (:REWRITE DM::SPLIT$-CASE-5-7))
 (11 5 (:REWRITE DM::SPLIT$-CASE-5-2))
 (10 2 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (9 9 (:REWRITE REDUCE-RATIONALP-+))
 (9 9 (:REWRITE REDUCE-RATIONALP-*))
 (9 9 (:REWRITE RATIONALP-MINUS-X))
 (9 9 (:META META-RATIONALP-CORRECT))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:REWRITE THE-FLOOR-BELOW))
 (8 8 (:REWRITE THE-FLOOR-ABOVE))
 (8 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 8 (:REWRITE SIMPLIFY-SUMS-<))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (8 8 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (8 8 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (8 8 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (8 8 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (8 8 (:REWRITE INTEGERP-<-CONSTANT))
 (8 8 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-2))
 (8 8 (:REWRITE DEFAULT-LESS-THAN-1))
 (8 8 (:REWRITE CONSTANT-<-INTEGERP))
 (8 8 (:REWRITE |(equal c (/ x))|))
 (8 8 (:REWRITE |(equal c (- x))|))
 (8 8 (:REWRITE |(equal (/ x) c)|))
 (8 8 (:REWRITE |(equal (/ x) (/ y))|))
 (8 8 (:REWRITE |(equal (- x) c)|))
 (8 8 (:REWRITE |(equal (- x) (- y))|))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (8 8 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< c (- x))|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (8 8 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (8 8 (:REWRITE |(< (/ x) (/ y))|))
 (8 8 (:REWRITE |(< (- x) c)|))
 (8 8 (:REWRITE |(< (- x) (- y))|))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (7 7 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:REWRITE DM::SPLIT$-CASE-5-3))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (6 6 (:REWRITE |(< (/ x) 0)|))
 (6 6 (:REWRITE |(< (* x y) 0)|))
 (4 2 (:REWRITE DM::INT-CADDR-TRIPP))
 (2 2 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2 2 (:REWRITE DM::ALL-INTEGERS-VALS))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 (2 1 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-9))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE DM::SHNFP-INT))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(DM::SPLIT$-CASE-5-10
 (15380 4 (:DEFINITION DM::EVALH))
 (10795 117 (:REWRITE ACL2-NUMBERP-X))
 (7882 117 (:REWRITE RATIONALP-X))
 (6198 3041 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (6174 141 (:REWRITE DEFAULT-PLUS-1))
 (5035 1609 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (4528 8 (:REWRITE DM::INTEGERP-EVALH))
 (4488 8 (:DEFINITION DM::SHFP))
 (4096 143 (:REWRITE DEFAULT-PLUS-2))
 (3825 3825 (:TYPE-PRESCRIPTION DM::ECP))
 (3140 67 (:REWRITE DEFAULT-TIMES-2))
 (2438 14 (:REWRITE |(+ (if a b c) x)|))
 (1960 694 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (1637 1637 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS))
 (1617 36 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1542 1542 (:TYPE-PRESCRIPTION DM::TRIPP))
 (1388 694 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (1239 309 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1239 309 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (950 65 (:REWRITE DEFAULT-TIMES-1))
 (944 472 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (894 309 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (894 309 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (894 309 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (894 309 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (894 309 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (894 309 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (894 5 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (892 16 (:REWRITE DEFAULT-EXPT-2))
 (867 5 (:REWRITE MOD-X-Y-=-X . 4))
 (867 5 (:REWRITE MOD-X-Y-=-X . 3))
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 (865 5 (:REWRITE MOD-ZERO . 3))
 (841 5 (:REWRITE DEFAULT-MOD-RATIO))
 (801 5 (:REWRITE MOD-ZERO . 4))
 (792 5 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (759 5 (:REWRITE RTL::MOD-DOES-NOTHING))
 (758 12 (:REWRITE |(* (if a b c) x)|))
 (535 295 (:REWRITE DEFAULT-CDR))
 (528 9 (:REWRITE |(* y x)|))
 (520 4 (:REWRITE DM::NTHCDR+))
 (513 49 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (505 25 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (498 10 (:REWRITE DEFAULT-EXPT-1))
 (420 210 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (413 49 (:REWRITE DEFAULT-LESS-THAN-1))
 (342 3 (:REWRITE |(* x (+ y z))|))
 (318 2 (:REWRITE |(* (* x y) z)|))
 (295 171 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (295 171 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (274 154 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (274 154 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (271 171 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (271 171 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (260 16 (:REWRITE ZP-OPEN))
 (239 49 (:REWRITE SIMPLIFY-SUMS-<))
 (202 202 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (202 202 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (202 202 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (202 171 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (194 2 (:REWRITE |(* y (* x z))|))
 (192 8 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (171 171 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (171 171 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (171 171 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (171 171 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (171 171 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (171 171 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (171 171 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (171 5 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (171 5 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (166 5 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (166 5 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (166 5 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (160 4 (:DEFINITION DM::ALL-INTEGERS))
 (154 154 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (149 59 (:REWRITE DM::INTEGERP-EC-X))
 (149 59 (:REWRITE DM::INT-CAR-TRIPP))
 (149 49 (:REWRITE DEFAULT-LESS-THAN-2))
 (148 10 (:REWRITE |(* 1 x)|))
 (146 146 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (146 146 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (142 93 (:META META-INTEGERP-CORRECT))
 (141 5 (:REWRITE DEFAULT-MOD-1))
 (126 42 (:REWRITE DM::SPLIT$-CASE-5-8))
 (122 5 (:REWRITE MOD-X-Y-=-X . 2))
 (116 48 (:REWRITE DM::INT-CADR-TRIPP))
 (110 8 (:DEFINITION NTH))
 (96 96 (:TYPE-PRESCRIPTION DM::SHFP))
 (96 32 (:REWRITE DM::SPLIT$-CASE-5-7))
 (94 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (93 93 (:REWRITE REDUCE-INTEGERP-+))
 (93 93 (:REWRITE INTEGERP-MINUS-X))
 (64 32 (:REWRITE DM::SHNFP-SHFP))
 (63 63 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (63 63 (:REWRITE NORMALIZE-ADDENDS))
 (52 4 (:REWRITE ZIP-OPEN))
 (49 49 (:REWRITE THE-FLOOR-BELOW))
 (49 49 (:REWRITE THE-FLOOR-ABOVE))
 (49 49 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (49 49 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (49 49 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (49 49 (:REWRITE INTEGERP-<-CONSTANT))
 (49 49 (:REWRITE CONSTANT-<-INTEGERP))
 (49 49 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (49 49 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (49 49 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (49 49 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (49 49 (:REWRITE |(< c (- x))|))
 (49 49 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (49 49 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (49 49 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (49 49 (:REWRITE |(< (/ x) (/ y))|))
 (49 49 (:REWRITE |(< (- x) c)|))
 (49 49 (:REWRITE |(< (- x) (- y))|))
 (46 4 (:REWRITE |(+ y (+ x z))|))
 (44 20 (:REWRITE DM::SPLIT$-CASE-5-2))
 (39 39 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (39 39 (:REWRITE REDUCE-RATIONALP-+))
 (39 39 (:REWRITE REDUCE-RATIONALP-*))
 (39 39 (:REWRITE RATIONALP-MINUS-X))
 (39 39 (:META META-RATIONALP-CORRECT))
 (36 36 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (36 36 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (36 36 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (36 36 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (36 36 (:REWRITE |(equal c (/ x))|))
 (36 36 (:REWRITE |(equal c (- x))|))
 (36 36 (:REWRITE |(equal (/ x) c)|))
 (36 36 (:REWRITE |(equal (/ x) (/ y))|))
 (36 36 (:REWRITE |(equal (- x) c)|))
 (36 36 (:REWRITE |(equal (- x) (- y))|))
 (35 35 (:TYPE-PRESCRIPTION NATP))
 (29 29 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (29 29 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (29 29 (:REWRITE |(< (/ x) 0)|))
 (29 29 (:REWRITE |(< (* x y) 0)|))
 (28 2 (:REWRITE |(expt 0 n)|))
 (26 26 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (25 25 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (25 25 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (25 25 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (22 10 (:LINEAR DM::P-IS-BIG))
 (18 9 (:REWRITE DEFAULT-DIVIDE))
 (16 8 (:REWRITE DM::INT-CADDR-TRIPP))
 (10 5 (:REWRITE DEFAULT-MOD-2))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (9 9 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (9 9 (:REWRITE |(< 0 (/ x))|))
 (9 9 (:REWRITE |(< 0 (* x y))|))
 (8 8 (:REWRITE |(expt 1/c n)|))
 (8 8 (:REWRITE |(expt (- x) n)|))
 (6 6 (:REWRITE |(< (+ c/d x) y)|))
 (6 6 (:REWRITE |(< (+ (- c) x) y)|))
 (5 5 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (5 5 (:REWRITE |(mod x (- y))| . 3))
 (5 5 (:REWRITE |(mod x (- y))| . 2))
 (5 5 (:REWRITE |(mod x (- y))| . 1))
 (5 5 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (5 5 (:REWRITE |(* c (* d x))|))
 (4 4 (:REWRITE DM::ALL-INTEGERS-VALS))
 (4 4 (:REWRITE |(* 0 x)|))
 (2 2 (:REWRITE DM::SHNFP-INT))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (2 2 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (1 1 (:REWRITE INTEGERP-/))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 (1 1 (:REWRITE |(< y (+ (- c) x))|))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 )
(DM::SPLIT$-CASE-5-11
 (4 4 (:DEFINITION MV-NTH))
 )
(DM::SPLIT$-CASE-5-12
 (140 70 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (85 85 (:TYPE-PRESCRIPTION DM::ECP))
 (60 10 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (35 35 (:TYPE-PRESCRIPTION DM::TRIPP))
 (30 15 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (30 15 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (20 10 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (20 10 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 )
(DM::SPLIT$-CASE-5-13
 (11 1 (:DEFINITION NTH))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 1 (:REWRITE DEFAULT-CDR))
 (2 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE NORMALIZE-ADDENDS))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE DEFAULT-PLUS-2))
 (1 1 (:REWRITE DEFAULT-PLUS-1))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(DM::SPLIT$-CASE-5-14
 (273606 12 (:DEFINITION DM::SPLIT$))
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 (158113 2331 (:REWRITE ACL2-NUMBERP-X))
 (87322 2211 (:REWRITE RATIONALP-X))
 (65351 743 (:REWRITE DEFAULT-LESS-THAN-2))
 (62128 31060 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
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 (49827 1513 (:REWRITE DEFAULT-PLUS-1))
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 (45671 647 (:REWRITE DEFAULT-LESS-THAN-1))
 (42966 21470 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (42940 21470 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (38016 384 (:REWRITE DEFAULT-MINUS))
 (37750 535 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (36836 17826 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (35500 17750 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (30119 1641 (:REWRITE DEFAULT-PLUS-2))
 (18185 1266 (:REWRITE DEFAULT-CAR))
 (8482 1979 (:REWRITE DEFAULT-CDR))
 (7376 6 (:DEFINITION DM::EVALH))
 (7181 279 (:REWRITE DEFAULT-TIMES-1))
 (6960 48 (:DEFINITION DM::NORM-EXPT))
 (6634 2214 (:REWRITE DM::INTEGERP-EC-X))
 (6634 2214 (:REWRITE DM::INT-CAR-TRIPP))
 (5634 1878 (:REWRITE DM::INT-CADR-TRIPP))
 (5185 71 (:REWRITE ZP-OPEN))
 (4896 240 (:REWRITE |(+ x (if a b c))|))
 (3511 535 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3000 48 (:REWRITE |(< x (if a b c))|))
 (2664 12 (:DEFINITION EVENP))
 (2323 2323 (:REWRITE REDUCE-INTEGERP-+))
 (2323 2323 (:REWRITE INTEGERP-MINUS-X))
 (2323 2323 (:META META-INTEGERP-CORRECT))
 (2211 2211 (:REWRITE REDUCE-RATIONALP-+))
 (2211 2211 (:REWRITE REDUCE-RATIONALP-*))
 (2211 2211 (:REWRITE RATIONALP-MINUS-X))
 (2211 2211 (:META META-RATIONALP-CORRECT))
 (1162 20 (:REWRITE DEFAULT-EXPT-2))
 (1152 44 (:REWRITE |(* (if a b c) x)|))
 (1051 285 (:REWRITE DEFAULT-TIMES-2))
 (1042 14 (:REWRITE DEFAULT-EXPT-1))
 (786 162 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (748 26 (:REWRITE |(+ (if a b c) x)|))
 (743 743 (:REWRITE THE-FLOOR-BELOW))
 (743 743 (:REWRITE THE-FLOOR-ABOVE))
 (624 6 (:REWRITE DM::NTHCDR+))
 (592 296 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (586 394 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (562 62 (:REWRITE |(* y x)|))
 (535 535 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (535 535 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (535 535 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (535 535 (:REWRITE |(equal c (/ x))|))
 (535 535 (:REWRITE |(equal c (- x))|))
 (535 535 (:REWRITE |(equal (/ x) c)|))
 (535 535 (:REWRITE |(equal (/ x) (/ y))|))
 (535 535 (:REWRITE |(equal (- x) c)|))
 (535 535 (:REWRITE |(equal (- x) (- y))|))
 (486 6 (:REWRITE DM::EVALH-POW-REWRITE))
 (478 478 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (478 478 (:REWRITE NORMALIZE-ADDENDS))
 (456 456 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (456 456 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (456 456 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (456 456 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (432 36 (:REWRITE |(* x (+ y z))|))
 (431 407 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (431 407 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (407 407 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (407 407 (:REWRITE INTEGERP-<-CONSTANT))
 (407 407 (:REWRITE CONSTANT-<-INTEGERP))
 (407 407 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (407 407 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (407 407 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (407 407 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (407 407 (:REWRITE |(< c (- x))|))
 (407 407 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (407 407 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (407 407 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (407 407 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (407 407 (:REWRITE |(< (/ x) (/ y))|))
 (407 407 (:REWRITE |(< (- x) c)|))
 (407 407 (:REWRITE |(< (- x) (- y))|))
 (400 13 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (394 394 (:REWRITE SIMPLIFY-SUMS-<))
 (361 13 (:DEFINITION DM::ALL-INTEGERS))
 (253 17 (:REWRITE DM::CONSP-NTHCDR))
 (162 162 (:REWRITE |(< 0 (/ x))|))
 (162 162 (:REWRITE |(< 0 (* x y))|))
 (150 150 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (122 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (122 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (122 8 (:REWRITE ZIP-OPEN))
 (115 115 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (114 114 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (114 114 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (114 114 (:REWRITE |(< (/ x) 0)|))
 (114 114 (:REWRITE |(< (* x y) 0)|))
 (110 10 (:DEFINITION NTH))
 (104 66 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-7))
 (96 96 (:TYPE-PRESCRIPTION DM::NORM-POP))
 (96 96 (:TYPE-PRESCRIPTION DM::NORM-MUL))
 (86 32 (:REWRITE DM::SHNFP-INT))
 (84 6 (:REWRITE |(+ y (+ x z))|))
 (50 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (50 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (50 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (50 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (50 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (50 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (50 50 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (48 48 (:TYPE-PRESCRIPTION ABS))
 (48 30 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (48 4 (:REWRITE DM::CAR-NTHCDR))
 (42 42 (:REWRITE |(< y (+ (- c) x))|))
 (42 42 (:REWRITE |(< x (+ c/d y))|))
 (38 38 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (38 38 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (38 38 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (38 38 (:TYPE-PRESCRIPTION EXPT))
 (28 2 (:REWRITE |(expt 0 n)|))
 (24 24 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (20 8 (:REWRITE DM::SPLIT$-CASE-5-2))
 (16 14 (:REWRITE |(* 1 x)|))
 (16 4 (:REWRITE DM::SPLIT$-CASE-5-7))
 (15 15 (:REWRITE DM::LEN-VALS))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (8 8 (:REWRITE |(expt 1/c n)|))
 (8 8 (:REWRITE |(expt (- x) n)|))
 (8 8 (:REWRITE |(* 0 x)|))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:REWRITE |(equal (+ (- c) x) y)|))
 )
(DM::SPLIT$-CASE-5-15
 (152 76 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (152 76 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (138 138 (:TYPE-PRESCRIPTION DM::ECP))
 (120 60 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (119 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (119 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (112 28 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (110 110 (:TYPE-PRESCRIPTION DM::TRIPP))
 (64 32 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (58 2 (:REWRITE ACL2-NUMBERP-X))
 (52 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (36 12 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (34 2 (:REWRITE RATIONALP-X))
 (32 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (32 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (32 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (32 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (32 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (32 29 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (28 28 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (28 28 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (23 1 (:REWRITE DEFAULT-EXPT-1))
 (13 13 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS))
 (11 1 (:DEFINITION NTHCDR))
 (11 1 (:DEFINITION NTH))
 (10 3 (:REWRITE DEFAULT-CAR))
 (5 3 (:REWRITE DEFAULT-CDR))
 (5 1 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (5 1 (:REWRITE |(+ y x)|))
 (4 1 (:REWRITE DEFAULT-EXPT-2))
 (3 3 (:REWRITE DEFAULT-PLUS-2))
 (3 3 (:REWRITE DEFAULT-PLUS-1))
 (3 1 (:REWRITE DM::INTEGERP-EC-X))
 (3 1 (:REWRITE DM::INT-CAR-TRIPP))
 (2 2 (:REWRITE ZP-OPEN))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE DM::SHNFP-INT))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE DM::ALL-INTEGERS-VALS))
 (1 1 (:REWRITE |(expt 1/c n)|))
 (1 1 (:REWRITE |(expt (- x) n)|))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (/ x) c)|))
 (1 1 (:REWRITE |(equal (/ x) (/ y))|))
 (1 1 (:REWRITE |(equal (- x) c)|))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE |(< (/ x) 0)|))
 (1 1 (:REWRITE |(< (* x y) 0)|))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(DM::SPLIT$-CASE-5-16)
(DM::SPLIT$-CASE-5-17
 (64 64 (:DEFINITION MV-NTH))
 (22 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (22 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (22 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (22 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (16 16 (:TYPE-PRESCRIPTION DM::TRIPP))
 (16 16 (:TYPE-PRESCRIPTION DM::ECP))
 (16 8 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (16 8 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (16 8 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (16 8 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (16 8 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (8 8 (:TYPE-PRESCRIPTION DM::SHNFP))
 (2 2 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2 2 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 )
(DM::SPLIT$-CASE-5-18
 (273606 12 (:DEFINITION DM::SPLIT$))
 (248832 48 (:DEFINITION DM::NORM-ADD))
 (158377 2343 (:REWRITE ACL2-NUMBERP-X))
 (87406 2223 (:REWRITE RATIONALP-X))
 (65353 745 (:REWRITE DEFAULT-LESS-THAN-2))
 (62348 31166 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (57118 57118 (:TYPE-PRESCRIPTION DM::ECP))
 (49923 1555 (:REWRITE DEFAULT-PLUS-1))
 (47828 47828 (:TYPE-PRESCRIPTION DM::TRIPP))
 (45673 649 (:REWRITE DEFAULT-LESS-THAN-1))
 (43066 21524 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (43048 21524 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (38016 384 (:REWRITE DEFAULT-MINUS))
 (37758 537 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (37024 17882 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (35624 17812 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (30333 1685 (:REWRITE DEFAULT-PLUS-2))
 (18313 1268 (:REWRITE DEFAULT-CAR))
 (8846 2002 (:REWRITE DEFAULT-CDR))
 (8414 6 (:DEFINITION DM::EVALH))
 (7185 287 (:REWRITE DEFAULT-TIMES-1))
 (6960 48 (:DEFINITION DM::NORM-EXPT))
 (6644 2216 (:REWRITE DM::INTEGERP-EC-X))
 (6644 2216 (:REWRITE DM::INT-CAR-TRIPP))
 (5652 1884 (:REWRITE DM::INT-CADR-TRIPP))
 (5183 69 (:REWRITE ZP-OPEN))
 (4896 240 (:REWRITE |(+ x (if a b c))|))
 (3513 537 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3000 48 (:REWRITE |(< x (if a b c))|))
 (2664 12 (:DEFINITION EVENP))
 (2333 2333 (:REWRITE REDUCE-INTEGERP-+))
 (2333 2333 (:REWRITE INTEGERP-MINUS-X))
 (2333 2333 (:META META-INTEGERP-CORRECT))
 (2223 2223 (:REWRITE REDUCE-RATIONALP-+))
 (2223 2223 (:REWRITE REDUCE-RATIONALP-*))
 (2223 2223 (:REWRITE RATIONALP-MINUS-X))
 (2223 2223 (:META META-RATIONALP-CORRECT))
 (1391 297 (:REWRITE DEFAULT-TIMES-2))
 (1202 46 (:REWRITE |(* (if a b c) x)|))
 (1184 16 (:REWRITE DEFAULT-EXPT-1))
 (1170 22 (:REWRITE DEFAULT-EXPT-2))
 (844 32 (:REWRITE |(+ (if a b c) x)|))
 (786 162 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (745 745 (:REWRITE THE-FLOOR-BELOW))
 (745 745 (:REWRITE THE-FLOOR-ABOVE))
 (624 6 (:REWRITE DM::NTHCDR+))
 (602 64 (:REWRITE |(* y x)|))
 (592 296 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (588 396 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (537 537 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (537 537 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (537 537 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (537 537 (:REWRITE |(equal c (/ x))|))
 (537 537 (:REWRITE |(equal c (- x))|))
 (537 537 (:REWRITE |(equal (/ x) c)|))
 (537 537 (:REWRITE |(equal (/ x) (/ y))|))
 (537 537 (:REWRITE |(equal (- x) c)|))
 (537 537 (:REWRITE |(equal (- x) (- y))|))
 (488 488 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (488 488 (:REWRITE NORMALIZE-ADDENDS))
 (486 6 (:REWRITE DM::EVALH-POW-REWRITE))
 (456 456 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (456 456 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (456 456 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (456 456 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (452 20 (:REWRITE DM::CONSP-NTHCDR))
 (433 409 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (433 409 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (432 36 (:REWRITE |(* x (+ y z))|))
 (409 409 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (409 409 (:REWRITE INTEGERP-<-CONSTANT))
 (409 409 (:REWRITE CONSTANT-<-INTEGERP))
 (409 409 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (409 409 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (409 409 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (409 409 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (409 409 (:REWRITE |(< c (- x))|))
 (409 409 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (409 409 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (409 409 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (409 409 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (409 409 (:REWRITE |(< (/ x) (/ y))|))
 (409 409 (:REWRITE |(< (- x) c)|))
 (409 409 (:REWRITE |(< (- x) (- y))|))
 (396 396 (:REWRITE SIMPLIFY-SUMS-<))
 (280 9 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (253 9 (:DEFINITION DM::ALL-INTEGERS))
 (166 10 (:REWRITE ZIP-OPEN))
 (162 162 (:REWRITE |(< 0 (/ x))|))
 (162 162 (:REWRITE |(< 0 (* x y))|))
 (150 150 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (116 116 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (116 116 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (116 116 (:REWRITE |(< (/ x) 0)|))
 (116 116 (:REWRITE |(< (* x y) 0)|))
 (115 115 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (102 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (96 96 (:TYPE-PRESCRIPTION DM::NORM-POP))
 (96 96 (:TYPE-PRESCRIPTION DM::NORM-MUL))
 (88 8 (:DEFINITION NTH))
 (86 32 (:REWRITE DM::SHNFP-INT))
 (86 4 (:REWRITE |(expt 0 n)|))
 (84 6 (:REWRITE |(+ y (+ x z))|))
 (76 38 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-7))
 (54 54 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (54 54 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (54 54 (:TYPE-PRESCRIPTION EXPT))
 (48 48 (:TYPE-PRESCRIPTION ABS))
 (42 42 (:REWRITE |(< y (+ (- c) x))|))
 (42 42 (:REWRITE |(< x (+ c/d y))|))
 (36 18 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (24 24 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (24 2 (:REWRITE DM::CAR-NTHCDR))
 (22 10 (:REWRITE DM::SPLIT$-CASE-5-2))
 (16 16 (:REWRITE DM::LEN-VALS))
 (16 16 (:REWRITE |(* 1 x)|))
 (16 4 (:REWRITE DM::SPLIT$-CASE-5-7))
 (10 10 (:TYPE-PRESCRIPTION NATP))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (10 10 (:REWRITE |(expt 1/c n)|))
 (10 10 (:REWRITE |(expt (- x) n)|))
 (10 10 (:REWRITE |(* 0 x)|))
 (6 6 (:REWRITE FOLD-CONSTS-IN-+))
 (6 6 (:REWRITE |(equal (+ (- c) x) y)|))
 )
(DM::SPLIT$-CASE-5-19
 (3928 12 (:LINEAR MOD-BOUNDS-3))
 (3260 520 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (2980 596 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (2980 596 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (2952 2952 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2952 2952 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2952 2952 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (2900 596 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (2900 596 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2389 93 (:REWRITE |(* y x)|))
 (2218 43 (:REWRITE MOD-ZERO . 3))
 (2030 58 (:REWRITE |(* (* x y) z)|))
 (1961 503 (:REWRITE DEFAULT-TIMES-2))
 (1950 313 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (1695 43 (:REWRITE DEFAULT-MOD-RATIO))
 (1548 31 (:REWRITE |(* x (+ y z))|))
 (1495 43 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (1426 71 (:REWRITE DEFAULT-PLUS-2))
 (1406 43 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (1344 43 (:REWRITE MOD-X-Y-=-X . 4))
 (1344 43 (:REWRITE MOD-X-Y-=-X . 3))
 (1211 71 (:REWRITE DEFAULT-PLUS-1))
 (1208 503 (:REWRITE DEFAULT-TIMES-1))
 (1167 43 (:REWRITE RTL::MOD-DOES-NOTHING))
 (936 24 (:LINEAR MOD-BOUNDS-2))
 (754 58 (:REWRITE |(* y (* x z))|))
 (725 43 (:REWRITE MOD-ZERO . 4))
 (692 213 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (596 596 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (596 596 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (596 596 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (596 596 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (596 596 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (574 43 (:REWRITE MOD-X-Y-=-X . 2))
 (520 520 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (520 520 (:TYPE-PRESCRIPTION NATP))
 (509 16 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (501 213 (:REWRITE DEFAULT-LESS-THAN-1))
 (367 86 (:META META-INTEGERP-CORRECT))
 (313 313 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (313 313 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (313 313 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
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(DM::SPLIT$-CASE-5-20
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(DM::SPLIT$-CASE-5-21
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(DM::SPLIT$-CASE-5-23
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(DM::SPLIT$-CASE-5-24
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(DM::SPLIT$-CASE-5
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(DM::SPLIT$-CASE-4-1
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 (2 2 (:REWRITE THE-FLOOR-ABOVE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (2 2 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2 2 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (2 2 (:REWRITE CONSTANT-<-INTEGERP))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2 2 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< c (- x))|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2 2 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (2 2 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (/ x) (/ y))|))
 (2 2 (:REWRITE |(< (- x) c)|))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE |(* c (expt d n))|))
 (1 1 (:REWRITE ZIP-OPEN))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
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(DM::SPLIT$-CASE-4-3
 (672 672 (:DEFINITION MV-NTH))
 )
(DM::SPLIT$-CASE-4-4
 (272479 18 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (143284 319 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (137069 18 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (96265 225 (:REWRITE MOD-ZERO . 3))
 (89407 17951 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (89407 17951 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (88219 17951 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (88219 17951 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (75061 75061 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (75061 75061 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (75061 75061 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (67260 228 (:REWRITE DEFAULT-MOD-RATIO))
 (50065 3714 (:REWRITE DEFAULT-TIMES-2))
 (47579 225 (:REWRITE MOD-X-Y-=-X . 4))
 (47579 225 (:REWRITE MOD-X-Y-=-X . 3))
 (47559 225 (:REWRITE MOD-X-Y-=-X-Y . 2))
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 (40637 225 (:REWRITE RTL::MOD-DOES-NOTHING))
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 (38967 1928 (:REWRITE DEFAULT-PLUS-2))
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 (34188 11034 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (31562 1189 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
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 (20128 3714 (:REWRITE DEFAULT-TIMES-1))
 (19323 1928 (:REWRITE DEFAULT-PLUS-1))
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 (13187 225 (:REWRITE MOD-X-Y-=-X . 2))
 (11034 11034 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (11034 11034 (:TYPE-PRESCRIPTION NATP))
 (8351 225 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (8351 225 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (7901 7901 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
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 (6154 214 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
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 (5208 128 (:LINEAR MOD-BOUNDS-2))
 (3950 214 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (2840 2840 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2778 225 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (2778 225 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (2778 225 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (2457 313 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2270 1870 (:REWRITE INTEGERP-MINUS-X))
 (2158 214 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (1652 11 (:REWRITE |(integerp (- x))|))
 (1514 1514 (:REWRITE |(* c (* d x))|))
 (1512 54 (:REWRITE DEFAULT-MINUS))
 (1381 1381 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1193 1193 (:REWRITE THE-FLOOR-BELOW))
 (1193 1193 (:REWRITE THE-FLOOR-ABOVE))
 (1192 1192 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1192 1192 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1191 1190 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1190 1190 (:REWRITE INTEGERP-<-CONSTANT))
 (1190 1190 (:REWRITE CONSTANT-<-INTEGERP))
 (1190 1190 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1190 1190 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1190 1190 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1190 1190 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1190 1190 (:REWRITE |(< c (- x))|))
 (1190 1190 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (1190 1190 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1190 1190 (:REWRITE |(< (/ x) (/ y))|))
 (1190 1190 (:REWRITE |(< (- x) c)|))
 (1190 1190 (:REWRITE |(< (- x) (- y))|))
 (834 567 (:REWRITE DEFAULT-DIVIDE))
 (823 823 (:REWRITE |(< (+ c/d x) y)|))
 (750 750 (:REWRITE INTEGERP-/))
 (704 704 (:REWRITE |(+ c (+ d x))|))
 (677 677 (:REWRITE FOLD-CONSTS-IN-+))
 (591 18 (:REWRITE |(equal (mod (+ x y) z) x)|))
 (566 566 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (485 485 (:REWRITE |(< (* x y) 0)|))
 (484 484 (:REWRITE |(< (/ x) 0)|))
 (483 483 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (483 483 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (347 228 (:REWRITE DEFAULT-MOD-2))
 (322 319 (:REWRITE |(equal (- x) (- y))|))
 (319 319 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (319 319 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (319 319 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (319 319 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (319 319 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (319 319 (:REWRITE |(equal c (/ x))|))
 (319 319 (:REWRITE |(equal c (- x))|))
 (319 319 (:REWRITE |(equal (/ x) c)|))
 (319 319 (:REWRITE |(equal (/ x) (/ y))|))
 (319 319 (:REWRITE |(equal (- x) c)|))
 (293 293 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (293 293 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (293 293 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (293 293 (:REWRITE |(< 0 (/ x))|))
 (293 293 (:REWRITE |(< 0 (* x y))|))
 (260 260 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (225 225 (:REWRITE |(mod x (- y))| . 3))
 (225 225 (:REWRITE |(mod x (- y))| . 2))
 (225 225 (:REWRITE |(mod x (- y))| . 1))
 (205 205 (:REWRITE |(equal (+ (- c) x) y)|))
 (189 189 (:REWRITE |(< y (+ (- c) x))|))
 (189 189 (:REWRITE |(< x (+ c/d y))|))
 (126 46 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (64 64 (:LINEAR RTL::MOD-BND-3))
 (54 6 (:TYPE-PRESCRIPTION FLOOR-ZERO . 2))
 (54 6 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 1))
 (54 6 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 1))
 (54 6 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 1))
 (54 6 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 1))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-ZERO . 3))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-ZERO . 1))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 3))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-POSITIVE . 2))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 3))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-NONPOSITIVE . 2))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 3))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-NONNEGATIVE . 2))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 3))
 (30 6 (:TYPE-PRESCRIPTION FLOOR-NEGATIVE . 2))
 (29 29 (:REWRITE |(- (* c x))|))
 (2 2 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (1 1 (:REWRITE |(< (* (/ x) y) 1) with (< x 0)|))
 )
(DM::SPLIT$-CASE-4-5
 (10168 26 (:REWRITE |(* y x)|))
 (8788 464 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (8742 52 (:REWRITE |(* x (+ y z))|))
 (7926 12 (:REWRITE MOD-ZERO . 3))
 (6328 12 (:REWRITE DEFAULT-MOD-RATIO))
 (4670 934 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (4670 934 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (4670 934 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (4670 934 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (4124 104 (:REWRITE DEFAULT-PLUS-2))
 (4015 4015 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4015 4015 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4015 4015 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (3834 12 (:REWRITE MOD-X-Y-=-X . 4))
 (3834 12 (:REWRITE MOD-X-Y-=-X . 3))
 (3528 26 (:REWRITE |(+ y (+ x z))|))
 (3512 4 (:LINEAR MOD-BOUNDS-3))
 (3432 12 (:REWRITE MOD-ZERO . 4))
 (3422 156 (:REWRITE DEFAULT-TIMES-2))
 (3412 12 (:REWRITE MOD-X-Y-=-X-Y . 2))
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 (2864 12 (:REWRITE RTL::MOD-DOES-NOTHING))
 (2756 84 (:META META-INTEGERP-CORRECT))
 (2626 64 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2116 64 (:REWRITE DEFAULT-LESS-THAN-1))
 (1954 1954 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1954 1954 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1954 1954 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1954 1954 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1954 1954 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1954 1954 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1954 1954 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1954 1954 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1920 104 (:REWRITE DEFAULT-PLUS-1))
 (1780 890 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (1582 156 (:REWRITE DEFAULT-TIMES-1))
 (1258 4 (:LINEAR RTL::MOD-BND-2))
 (1172 12 (:REWRITE MOD-X-Y-=-X . 2))
 (934 934 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (934 934 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (934 934 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
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 (934 934 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (914 12 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (890 890 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (890 890 (:TYPE-PRESCRIPTION NATP))
 (708 12 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (708 12 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (696 12 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (696 12 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (696 12 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (632 12 (:REWRITE DEFAULT-MOD-1))
 (558 64 (:REWRITE DEFAULT-LESS-THAN-2))
 (494 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (472 8 (:LINEAR MOD-BOUNDS-2))
 (464 464 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (464 464 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (464 464 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (130 130 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (84 84 (:REWRITE REDUCE-INTEGERP-+))
 (84 84 (:REWRITE INTEGERP-MINUS-X))
 (78 78 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (78 78 (:REWRITE NORMALIZE-ADDENDS))
 (64 64 (:REWRITE THE-FLOOR-BELOW))
 (64 64 (:REWRITE THE-FLOOR-ABOVE))
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 (64 64 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (64 64 (:REWRITE INTEGERP-<-CONSTANT))
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 (64 64 (:REWRITE |(< (- x) (- y))|))
 (52 52 (:REWRITE |(* c (* d x))|))
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 (44 44 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (44 44 (:REWRITE |(< (+ c/d x) y)|))
 (44 44 (:REWRITE |(< (+ (- c) x) y)|))
 (28 28 (:REWRITE INTEGERP-/))
 (26 26 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (26 26 (:REWRITE FOLD-CONSTS-IN-+))
 (26 26 (:REWRITE |(+ c (+ d x))|))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (24 24 (:REWRITE |(< (/ x) 0)|))
 (24 24 (:REWRITE |(< (* x y) 0)|))
 (24 12 (:REWRITE DEFAULT-MOD-2))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (20 20 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (20 20 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (20 20 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (20 20 (:REWRITE |(equal c (/ x))|))
 (20 20 (:REWRITE |(equal c (- x))|))
 (20 20 (:REWRITE |(equal (/ x) c)|))
 (20 20 (:REWRITE |(equal (/ x) (/ y))|))
 (20 20 (:REWRITE |(equal (- x) c)|))
 (20 20 (:REWRITE |(equal (- x) (- y))|))
 (20 20 (:REWRITE |(< 0 (/ x))|))
 (20 20 (:REWRITE |(< 0 (* x y))|))
 (14 14 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (12 12 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (12 12 (:REWRITE |(mod x (- y))| . 3))
 (12 12 (:REWRITE |(mod x (- y))| . 2))
 (12 12 (:REWRITE |(mod x (- y))| . 1))
 (12 12 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (12 12 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (12 12 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (12 12 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (10 10 (:REWRITE |(equal (+ (- c) x) y)|))
 (10 10 (:REWRITE |(< y (+ (- c) x))|))
 (10 10 (:REWRITE |(< x (+ c/d y))|))
 (9 9 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (4 4 (:LINEAR RTL::MOD-BND-3))
 )
(DM::SPLIT$-CASE-4-6
 (312 312 (:DEFINITION MV-NTH))
 )
(DM::SPLIT$-CASE-4-7
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 (23 23 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
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 (23 23 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (16 16 (:REWRITE DEFAULT-TIMES-2))
 (16 16 (:REWRITE DEFAULT-TIMES-1))
 (10 10 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (9 9 (:REWRITE NORMALIZE-ADDENDS))
 (9 9 (:REWRITE DEFAULT-PLUS-2))
 (9 9 (:REWRITE DEFAULT-PLUS-1))
 (7 7 (:REWRITE THE-FLOOR-BELOW))
 (7 7 (:REWRITE THE-FLOOR-ABOVE))
 (7 7 (:REWRITE DEFAULT-LESS-THAN-2))
 (7 7 (:REWRITE DEFAULT-LESS-THAN-1))
 (7 7 (:REWRITE |(< (* x y) 0)|))
 (6 6 (:REWRITE SIMPLIFY-SUMS-<))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (6 6 (:REWRITE REMOVE-STRICT-INEQUALITIES))
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 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (6 6 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (6 6 (:REWRITE INTEGERP-<-CONSTANT))
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 (6 6 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
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 )
(DM::SPLIT$-CASE-4-8
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 (224 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
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 (221 221 (:REWRITE THE-FLOOR-BELOW))
 (221 221 (:REWRITE THE-FLOOR-ABOVE))
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 (221 221 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (221 221 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
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 (221 221 (:REWRITE |(< (/ x) (/ y))|))
 (221 221 (:REWRITE |(< (- x) c)|))
 (221 221 (:REWRITE |(< (- x) (- y))|))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (89 89 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (66 66 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (66 66 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
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 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
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 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (44 44 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (44 44 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (44 44 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (44 44 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (23 23 (:REWRITE |(< (/ x) 0)|))
 (23 23 (:REWRITE |(< (* x y) 0)|))
 (22 22 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (22 22 (:LINEAR EXPT-LINEAR-UPPER-<))
 (22 22 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (22 22 (:LINEAR EXPT-LINEAR-LOWER-<))
 (14 4 (:REWRITE DEFAULT-EXPT-1))
 (9 9 (:REWRITE DEFAULT-TIMES-2))
 (9 9 (:REWRITE DEFAULT-TIMES-1))
 (8 4 (:REWRITE DEFAULT-EXPT-2))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DEFAULT-PLUS-2))
 (4 4 (:REWRITE DEFAULT-PLUS-1))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (3 3 (:META META-INTEGERP-CORRECT))
 )
(DM::SPLIT$-CASE-4-9
 (219093 273 (:REWRITE RTL::MOD-DOES-NOTHING))
 (61236 1626 (:LINEAR EXPT-<=-1-ONE))
 (46954 1626 (:LINEAR EXPT->=-1-TWO))
 (46954 1626 (:LINEAR EXPT->-1-TWO))
 (46954 1626 (:LINEAR EXPT-<-1-ONE))
 (45186 1626 (:LINEAR EXPT-X->=-X))
 (45186 1626 (:LINEAR EXPT->=-1-ONE))
 (45186 1626 (:LINEAR EXPT-<=-1-TWO))
 (44908 1626 (:LINEAR EXPT-X->-X))
 (44908 1626 (:LINEAR EXPT->-1-ONE))
 (44908 1626 (:LINEAR EXPT-<-1-TWO))
 (37773 273 (:REWRITE MOD-ZERO . 4))
 (35247 273 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (34097 273 (:REWRITE MOD-X-Y-=-X . 4))
 (34097 273 (:REWRITE MOD-X-Y-=-X . 3))
 (32127 273 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (22203 4253 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (19508 18204 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (19508 18204 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (19097 273 (:REWRITE MOD-ZERO . 3))
 (18204 18204 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (18204 18204 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (18204 18204 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (18204 18204 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (18204 18204 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (17826 1540 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (16139 4253 (:REWRITE DEFAULT-LESS-THAN-1))
 (14223 273 (:REWRITE DEFAULT-MOD-RATIO))
 (12481 950 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (11084 11084 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (11084 11084 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (11084 11084 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (9729 4253 (:REWRITE DEFAULT-LESS-THAN-2))
 (9613 4253 (:REWRITE SIMPLIFY-SUMS-<))
 (8782 1229 (:REWRITE DEFAULT-TIMES-2))
 (8782 1229 (:REWRITE DEFAULT-TIMES-1))
 (8200 1640 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (8200 1640 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (8176 1640 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (8176 1640 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (8064 92 (:LINEAR MOD-BOUNDS-3))
 (7912 273 (:REWRITE MOD-X-Y-=-X . 2))
 (5420 220 (:REWRITE |(equal (expt x n) 0)|))
 (5153 273 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (5153 273 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (4253 4253 (:REWRITE THE-FLOOR-BELOW))
 (4253 4253 (:REWRITE THE-FLOOR-ABOVE))
 (4253 4253 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4253 4253 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4253 4253 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4253 4253 (:REWRITE INTEGERP-<-CONSTANT))
 (4253 4253 (:REWRITE CONSTANT-<-INTEGERP))
 (4253 4253 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4253 4253 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4253 4253 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4253 4253 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4253 4253 (:REWRITE |(< c (- x))|))
 (4253 4253 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (4253 4253 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (4253 4253 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (4253 4253 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4253 4253 (:REWRITE |(< (/ x) (/ y))|))
 (4253 4253 (:REWRITE |(< (- x) c)|))
 (4253 4253 (:REWRITE |(< (- x) (- y))|))
 (4113 273 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (4113 273 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (4113 273 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (3467 273 (:REWRITE DEFAULT-MOD-1))
 (3384 184 (:LINEAR MOD-BOUNDS-2))
 (3252 3252 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (3252 3252 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (3252 3252 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (3252 3252 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (2280 24 (:REWRITE MOD-POSITIVE . 3))
 (1977 1977 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1640 1640 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (1640 1640 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (1640 1640 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (1640 1640 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (1640 1640 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (1626 1626 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (1626 1626 (:LINEAR EXPT-LINEAR-UPPER-<))
 (1626 1626 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (1626 1626 (:LINEAR EXPT-LINEAR-LOWER-<))
 (1540 1540 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (1218 609 (:REWRITE DEFAULT-DIVIDE))
 (1146 1146 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1146 1146 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1146 1146 (:REWRITE |(< 0 (/ x))|))
 (1146 1146 (:REWRITE |(< 0 (* x y))|))
 (1102 619 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1040 273 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (1040 273 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (1040 273 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (950 950 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (950 950 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (950 950 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (835 835 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (835 835 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (835 835 (:REWRITE |(equal c (/ x))|))
 (835 835 (:REWRITE |(equal c (- x))|))
 (835 835 (:REWRITE |(equal (/ x) c)|))
 (835 835 (:REWRITE |(equal (/ x) (/ y))|))
 (835 835 (:REWRITE |(equal (- x) c)|))
 (835 835 (:REWRITE |(equal (- x) (- y))|))
 (823 823 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (823 823 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (823 823 (:REWRITE |(< (/ x) 0)|))
 (823 823 (:REWRITE |(< (* x y) 0)|))
 (619 619 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (619 619 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (619 619 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (613 613 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (609 609 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (546 273 (:REWRITE DEFAULT-MOD-2))
 (498 24 (:REWRITE MOD-POSITIVE . 2))
 (368 8 (:REWRITE ZP-OPEN))
 (359 359 (:REWRITE REDUCE-INTEGERP-+))
 (359 359 (:REWRITE INTEGERP-MINUS-X))
 (359 359 (:META META-INTEGERP-CORRECT))
 (273 273 (:REWRITE |(mod x (- y))| . 3))
 (273 273 (:REWRITE |(mod x (- y))| . 2))
 (273 273 (:REWRITE |(mod x (- y))| . 1))
 (268 8 (:REWRITE DM::MOD-EXPT-REWRITE-2))
 (268 8 (:REWRITE DM::MOD-EXPT-REWRITE-1))
 (108 8 (:REWRITE MOD-THEOREM-TWO))
 (84 84 (:LINEAR RTL::MOD-BND-3))
 (68 5 (:REWRITE DEFAULT-EXPT-1))
 (24 24 (:REWRITE MOD-POSITIVE . 1))
 (13 13 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (13 5 (:REWRITE DEFAULT-EXPT-2))
 (8 8 (:TYPE-PRESCRIPTION ZP))
 (8 8 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (8 8 (:REWRITE |(< 0 (* x (/ y))) rationalp (* x (/ y))|))
 (6 6 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DEFAULT-PLUS-2))
 (4 4 (:REWRITE DEFAULT-PLUS-1))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 )
(DM::SPLIT$-CASE-4-10
 (1244 22 (:LINEAR EXPT-<=-1-ONE))
 (1224 22 (:LINEAR EXPT->=-1-TWO))
 (1224 22 (:LINEAR EXPT->-1-TWO))
 (1224 22 (:LINEAR EXPT-<-1-ONE))
 (1164 22 (:LINEAR EXPT-X->=-X))
 (1164 22 (:LINEAR EXPT->=-1-ONE))
 (1164 22 (:LINEAR EXPT-<=-1-TWO))
 (1144 22 (:LINEAR EXPT-X->-X))
 (1144 22 (:LINEAR EXPT->-1-ONE))
 (1144 22 (:LINEAR EXPT-<-1-TWO))
 (421 221 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (341 221 (:REWRITE DEFAULT-LESS-THAN-2))
 (301 221 (:REWRITE DEFAULT-LESS-THAN-1))
 (224 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (224 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (221 221 (:REWRITE THE-FLOOR-BELOW))
 (221 221 (:REWRITE THE-FLOOR-ABOVE))
 (221 221 (:REWRITE SIMPLIFY-SUMS-<))
 (221 221 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (221 221 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (221 221 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (221 221 (:REWRITE INTEGERP-<-CONSTANT))
 (221 221 (:REWRITE CONSTANT-<-INTEGERP))
 (221 221 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (221 221 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (221 221 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (221 221 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (221 221 (:REWRITE |(< c (- x))|))
 (221 221 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (221 221 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (221 221 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (221 221 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (221 221 (:REWRITE |(< (/ x) (/ y))|))
 (221 221 (:REWRITE |(< (- x) c)|))
 (221 221 (:REWRITE |(< (- x) (- y))|))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (89 89 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (66 66 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (66 66 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (66 66 (:REWRITE |(< 0 (/ x))|))
 (66 66 (:REWRITE |(< 0 (* x y))|))
 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (54 54 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (44 44 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (44 44 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (44 44 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (44 44 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (23 23 (:REWRITE |(< (/ x) 0)|))
 (23 23 (:REWRITE |(< (* x y) 0)|))
 (22 22 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (22 22 (:LINEAR EXPT-LINEAR-UPPER-<))
 (22 22 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (22 22 (:LINEAR EXPT-LINEAR-LOWER-<))
 (14 4 (:REWRITE DEFAULT-EXPT-1))
 (13 4 (:REWRITE DEFAULT-EXPT-2))
 (9 9 (:REWRITE DEFAULT-TIMES-2))
 (9 9 (:REWRITE DEFAULT-TIMES-1))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:REWRITE DEFAULT-PLUS-2))
 (6 6 (:REWRITE DEFAULT-PLUS-1))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (4 4 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (3 3 (:META META-INTEGERP-CORRECT))
 )
(DM::SPLIT$-CASE-4-11)
(DM::SPLIT$-CASE-4-12
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (38 38 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (26 26 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (26 26 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (26 26 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (26 26 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (13 13 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (10 10 (:REWRITE DEFAULT-TIMES-2))
 (10 10 (:REWRITE DEFAULT-TIMES-1))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (6 6 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE DEFAULT-PLUS-2))
 (6 6 (:REWRITE DEFAULT-PLUS-1))
 (6 6 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE THE-FLOOR-BELOW))
 (5 5 (:REWRITE THE-FLOOR-ABOVE))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-2))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-1))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (4 4 (:REWRITE SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (4 4 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
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 (4 4 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (4 4 (:REWRITE |(< (/ x) (/ y))|))
 (4 4 (:REWRITE |(< (- x) c)|))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (3 3 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (2 2 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:REWRITE DEFAULT-EXPT-2))
 (1 1 (:REWRITE DEFAULT-EXPT-1))
 (1 1 (:REWRITE |(expt 1/c n)|))
 (1 1 (:REWRITE |(expt (- x) n)|))
 )
(DM::SPLIT$-CASE-4-13)
(DM::SPLIT$-CASE-4-14
 (206919 726 (:REWRITE RATIONALP-X))
 (198381 504 (:REWRITE DM::INTEGERP-EVALH))
 (195861 504 (:DEFINITION DM::SHFP))
 (182703 522 (:REWRITE ACL2-NUMBERP-X))
 (111285 45 (:DEFINITION DM::EVALH))
 (63738 2034 (:REWRITE DEFAULT-TIMES-1))
 (53379 723 (:REWRITE DEFAULT-PLUS-2))
 (47688 2079 (:REWRITE DEFAULT-TIMES-2))
 (37926 16281 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (32838 726 (:REWRITE REDUCE-RATIONALP-*))
 (30858 30858 (:TYPE-PRESCRIPTION DM::ECP))
 (30675 1761 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (29619 12939 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (27144 144 (:DEFINITION RFIX))
 (25878 12939 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (25053 25053 (:TYPE-PRESCRIPTION DM::TRIPP))
 (24984 48 (:LINEAR MOD-BOUNDS-2))
 (24354 7758 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (22827 21 (:REWRITE MOD-X-Y-=-X-Y . 1))
 (20076 20076 (:TYPE-PRESCRIPTION DM::THETA))
 (18987 13119 (:REWRITE DEFAULT-CDR))
 (16203 1914 (:REWRITE DEFAULT-LESS-THAN-1))
 (16110 129 (:REWRITE RTL::MOD-DOES-NOTHING))
 (15516 7758 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (13662 6765 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (13398 129 (:REWRITE MOD-X-Y-=-X . 3))
 (12774 24 (:LINEAR MOD-BOUNDS-3))
 (12681 129 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (11742 129 (:REWRITE MOD-X-Y-=-X . 4))
 (11391 1971 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (11391 1971 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (11004 21 (:REWRITE MOD-X-Y-=-X+Y . 1))
 (10782 10782 (:TYPE-PRESCRIPTION DM::SHNFP))
 (10197 129 (:REWRITE MOD-ZERO . 4))
 (8163 3384 (:REWRITE DEFAULT-CAR))
 (7833 6591 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (7833 6591 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
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 (7833 6591 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (7545 129 (:REWRITE MOD-ZERO . 3))
 (7329 7329 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (7329 7329 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (7329 7329 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (6765 6765 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS))
 (6699 1971 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (6699 1971 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (6591 6591 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (6591 6591 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (6402 1740 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6048 6048 (:TYPE-PRESCRIPTION DM::SHFP))
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 (4743 129 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (4623 1899 (:REWRITE SIMPLIFY-SUMS-<))
 (4320 45 (:REWRITE DM::EVALH-POW-REWRITE))
 (4032 2016 (:REWRITE DM::SHNFP-SHFP))
 (3960 45 (:DEFINITION EQL))
 (3870 678 (:REWRITE DEFAULT-PLUS-1))
 (3507 1971 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (3507 1971 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (3507 1971 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (3507 1971 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (3507 1971 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (3465 90 (:REWRITE |(+ (if a b c) x)|))
 (3375 135 (:REWRITE DEFAULT-EXPT-2))
 (3348 1812 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (3231 1914 (:REWRITE DEFAULT-LESS-THAN-2))
 (3051 1413 (:REWRITE DM::INTEGERP-EC-X))
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 (255 255 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (255 255 (:REWRITE |(< 0 (/ x))|))
 (255 255 (:REWRITE |(< 0 (* x y))|))
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 (21 21 (:REWRITE |(+ c (+ d x))|))
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 (88 88 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (88 88 (:REWRITE |(< (+ c/d x) y)|))
 (88 88 (:REWRITE |(< (+ (- c) x) y)|))
 (56 56 (:REWRITE INTEGERP-/))
 (52 52 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (52 52 (:REWRITE FOLD-CONSTS-IN-+))
 (52 52 (:REWRITE |(+ c (+ d x))|))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (48 48 (:REWRITE |(< (/ x) 0)|))
 (48 48 (:REWRITE |(< (* x y) 0)|))
 (48 24 (:REWRITE DEFAULT-MOD-2))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (40 40 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (40 40 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (40 40 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (40 40 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (40 40 (:REWRITE |(equal c (/ x))|))
 (40 40 (:REWRITE |(equal c (- x))|))
 (40 40 (:REWRITE |(equal (/ x) c)|))
 (40 40 (:REWRITE |(equal (/ x) (/ y))|))
 (40 40 (:REWRITE |(equal (- x) c)|))
 (40 40 (:REWRITE |(equal (- x) (- y))|))
 (40 40 (:REWRITE |(< 0 (/ x))|))
 (40 40 (:REWRITE |(< 0 (* x y))|))
 (28 28 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (24 24 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (24 24 (:REWRITE |(mod x (- y))| . 3))
 (24 24 (:REWRITE |(mod x (- y))| . 2))
 (24 24 (:REWRITE |(mod x (- y))| . 1))
 (24 24 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (24 24 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (24 24 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (24 24 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (20 20 (:REWRITE |(equal (+ (- c) x) y)|))
 (20 20 (:REWRITE |(< y (+ (- c) x))|))
 (20 20 (:REWRITE |(< x (+ c/d y))|))
 (8 8 (:LINEAR RTL::MOD-BND-3))
 )
(DM::SPLIT$-CASE-3-2
 (264 264 (:DEFINITION MV-NTH))
 )
(DM::SPLIT$-CASE-3-3
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 )
(DM::SPLIT$-CASE-3-4
 (1244 22 (:LINEAR EXPT-<=-1-ONE))
 (1224 22 (:LINEAR EXPT->=-1-TWO))
 (1224 22 (:LINEAR EXPT->-1-TWO))
 (1224 22 (:LINEAR EXPT-<-1-ONE))
 (1164 22 (:LINEAR EXPT-X->=-X))
 (1164 22 (:LINEAR EXPT->=-1-ONE))
 (1164 22 (:LINEAR EXPT-<=-1-TWO))
 (1144 22 (:LINEAR EXPT-X->-X))
 (1144 22 (:LINEAR EXPT->-1-ONE))
 (1144 22 (:LINEAR EXPT-<-1-TWO))
 (421 221 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (341 221 (:REWRITE DEFAULT-LESS-THAN-2))
 (301 221 (:REWRITE DEFAULT-LESS-THAN-1))
 (221 221 (:REWRITE THE-FLOOR-BELOW))
 (221 221 (:REWRITE THE-FLOOR-ABOVE))
 (221 221 (:REWRITE SIMPLIFY-SUMS-<))
 (221 221 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (221 221 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (221 221 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (221 221 (:REWRITE INTEGERP-<-CONSTANT))
 (221 221 (:REWRITE CONSTANT-<-INTEGERP))
 (221 221 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (221 221 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (221 221 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (221 221 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (221 221 (:REWRITE |(< c (- x))|))
 (221 221 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (221 221 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (221 221 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (221 221 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (221 221 (:REWRITE |(< (/ x) (/ y))|))
 (221 221 (:REWRITE |(< (- x) c)|))
 (221 221 (:REWRITE |(< (- x) (- y))|))
 (212 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (212 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (208 208 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (89 89 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (66 66 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (66 66 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (66 66 (:REWRITE |(< 0 (/ x))|))
 (66 66 (:REWRITE |(< 0 (* x y))|))
 (44 44 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (44 44 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (44 44 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (44 44 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (25 25 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (25 25 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (25 25 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (25 25 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (23 23 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (23 23 (:REWRITE |(< (/ x) 0)|))
 (23 23 (:REWRITE |(< (* x y) 0)|))
 (22 22 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (22 22 (:LINEAR EXPT-LINEAR-UPPER-<))
 (22 22 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (22 22 (:LINEAR EXPT-LINEAR-LOWER-<))
 (14 4 (:REWRITE DEFAULT-EXPT-1))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (5 5 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (5 5 (:REWRITE DEFAULT-TIMES-2))
 (5 5 (:REWRITE DEFAULT-TIMES-1))
 (4 4 (:REWRITE DEFAULT-EXPT-2))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (3 3 (:META META-INTEGERP-CORRECT))
 (2 2 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 )
(DM::SPLIT$-CASE-3-5
 (50932 145 (:REWRITE RTL::MOD-DOES-NOTHING))
 (32996 998 (:LINEAR EXPT-<=-1-ONE))
 (25846 998 (:LINEAR EXPT->=-1-TWO))
 (25846 998 (:LINEAR EXPT->-1-TWO))
 (25846 998 (:LINEAR EXPT-<-1-ONE))
 (24890 998 (:LINEAR EXPT-X->=-X))
 (24890 998 (:LINEAR EXPT->=-1-ONE))
 (24890 998 (:LINEAR EXPT-<=-1-TWO))
 (24724 998 (:LINEAR EXPT-X->-X))
 (24724 998 (:LINEAR EXPT->-1-ONE))
 (24724 998 (:LINEAR EXPT-<-1-TWO))
 (20180 145 (:REWRITE MOD-ZERO . 4))
 (19387 145 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (18825 145 (:REWRITE MOD-X-Y-=-X . 4))
 (18825 145 (:REWRITE MOD-X-Y-=-X . 3))
 (17579 145 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (12493 2547 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (11225 145 (:REWRITE MOD-ZERO . 3))
 (10068 10060 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (10068 10060 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (10060 10060 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (10060 10060 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (10060 10060 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (10060 10060 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (10060 10060 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (9141 2547 (:REWRITE DEFAULT-LESS-THAN-1))
 (6983 145 (:REWRITE DEFAULT-MOD-RATIO))
 (6793 542 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (5798 538 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (5619 2547 (:REWRITE SIMPLIFY-SUMS-<))
 (5311 2547 (:REWRITE DEFAULT-LESS-THAN-2))
 (4656 695 (:REWRITE DEFAULT-TIMES-2))
 (4656 695 (:REWRITE DEFAULT-TIMES-1))
 (4436 48 (:LINEAR MOD-BOUNDS-3))
 (4430 4430 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (4430 4430 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (4430 4430 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (3883 136 (:REWRITE |(equal (expt x n) 0)|))
 (3400 145 (:REWRITE MOD-X-Y-=-X . 2))
 (3110 622 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (3110 622 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (3086 622 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (3086 622 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (2547 2547 (:REWRITE THE-FLOOR-BELOW))
 (2547 2547 (:REWRITE THE-FLOOR-ABOVE))
 (2547 2547 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (2547 2547 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (2547 2547 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (2547 2547 (:REWRITE INTEGERP-<-CONSTANT))
 (2547 2547 (:REWRITE CONSTANT-<-INTEGERP))
 (2547 2547 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (2547 2547 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (2547 2547 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (2547 2547 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (2547 2547 (:REWRITE |(< c (- x))|))
 (2547 2547 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (2547 2547 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (2547 2547 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (2547 2547 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (2547 2547 (:REWRITE |(< (/ x) (/ y))|))
 (2547 2547 (:REWRITE |(< (- x) c)|))
 (2547 2547 (:REWRITE |(< (- x) (- y))|))
 (2521 145 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (2521 145 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (2065 145 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (2065 145 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (2065 145 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (2023 1996 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (2020 1996 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (1996 1996 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (1996 1996 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1856 96 (:LINEAR MOD-BOUNDS-2))
 (1651 145 (:REWRITE DEFAULT-MOD-1))
 (1182 1182 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1140 12 (:REWRITE MOD-POSITIVE . 3))
 (998 998 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (998 998 (:LINEAR EXPT-LINEAR-UPPER-<))
 (998 998 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (998 998 (:LINEAR EXPT-LINEAR-LOWER-<))
 (786 786 (:TYPE-PRESCRIPTION NOT-INTEGERP-4E))
 (786 786 (:TYPE-PRESCRIPTION NOT-INTEGERP-3E))
 (786 786 (:TYPE-PRESCRIPTION NOT-INTEGERP-2E))
 (786 786 (:TYPE-PRESCRIPTION NOT-INTEGERP-1E))
 (683 683 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (683 683 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (683 683 (:REWRITE |(< 0 (/ x))|))
 (683 683 (:REWRITE |(< 0 (* x y))|))
 (682 341 (:REWRITE DEFAULT-DIVIDE))
 (622 622 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (622 622 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (622 622 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (622 622 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (622 622 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (542 542 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (542 542 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (542 542 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (538 538 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (538 538 (:TYPE-PRESCRIPTION NATP))
 (537 370 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (506 506 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (506 506 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (506 506 (:REWRITE |(equal c (/ x))|))
 (506 506 (:REWRITE |(equal c (- x))|))
 (506 506 (:REWRITE |(equal (/ x) c)|))
 (506 506 (:REWRITE |(equal (/ x) (/ y))|))
 (506 506 (:REWRITE |(equal (- x) c)|))
 (506 506 (:REWRITE |(equal (- x) (- y))|))
 (495 495 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (495 495 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (495 495 (:REWRITE |(< (/ x) 0)|))
 (495 495 (:REWRITE |(< (* x y) 0)|))
 (456 145 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (456 145 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (456 145 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (370 370 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (370 370 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (370 370 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (351 351 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (341 341 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (290 145 (:REWRITE DEFAULT-MOD-2))
 (222 12 (:REWRITE MOD-POSITIVE . 2))
 (199 199 (:REWRITE REDUCE-INTEGERP-+))
 (199 199 (:REWRITE INTEGERP-MINUS-X))
 (199 199 (:META META-INTEGERP-CORRECT))
 (164 21 (:REWRITE DEFAULT-EXPT-1))
 (145 145 (:REWRITE |(mod x (- y))| . 3))
 (145 145 (:REWRITE |(mod x (- y))| . 2))
 (145 145 (:REWRITE |(mod x (- y))| . 1))
 (53 21 (:REWRITE DEFAULT-EXPT-2))
 (44 44 (:LINEAR RTL::MOD-BND-3))
 (20 20 (:REWRITE |(equal (* x y) 0)|))
 (12 12 (:REWRITE MOD-POSITIVE . 1))
 (12 12 (:REWRITE |(expt 1/c n)|))
 (12 12 (:REWRITE |(expt (- x) n)|))
 (10 10 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (9 9 (:REWRITE |(expt c (* d n))|))
 (8 8 (:REWRITE |(* c (* d x))|))
 (6 6 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (6 6 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 )
(DM::SPLIT$-CASE-3-6)
(DM::SPLIT$-CASE-3-7)
(DM::SPLIT$-CASE-3-8)
(DM::SPLIT$-CASE-3-9)
(DM::SPLIT$-CASE-3-10
 (60 60 (:DEFINITION MV-NTH))
 )
(DM::SPLIT$-CASE-3-11
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (2 2 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 )
(DM::SPLIT$-CASE-3-12
 (1396 1396 (:DEFINITION MV-NTH))
 )
(DM::SPLIT$-CASE-3-13
 (39135 227 (:REWRITE ACL2-NUMBERP-X))
 (34772 217 (:REWRITE RATIONALP-X))
 (29506 76 (:REWRITE DM::INTEGERP-EVALH))
 (28640 64 (:DEFINITION DM::SHFP))
 (11488 5724 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (10368 2 (:DEFINITION DM::NORM-ADD))
 (9357 9357 (:TYPE-PRESCRIPTION DM::ECP))
 (6511 6511 (:TYPE-PRESCRIPTION DM::TRIPP))
 (6325 3117 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (6234 3117 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (5764 2272 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (4128 2064 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (4084 191 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3298 250 (:REWRITE DEFAULT-PLUS-1))
 (3292 1890 (:REWRITE DEFAULT-CDR))
 (2893 193 (:REWRITE DEFAULT-LESS-THAN-2))
 (2448 557 (:REWRITE DEFAULT-CAR))
 (2069 189 (:REWRITE DEFAULT-LESS-THAN-1))
 (1584 16 (:REWRITE DEFAULT-MINUS))
 (1332 444 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (1116 20 (:REWRITE DEFAULT-EXPT-1))
 (1070 20 (:REWRITE DM::EVALH-POW-REWRITE))
 (1014 42 (:REWRITE ZP-OPEN))
 (953 11 (:DEFINITION EQL))
 (869 353 (:REWRITE DM::INTEGERP-EC-X))
 (869 353 (:REWRITE DM::INT-CAR-TRIPP))
 (780 780 (:TYPE-PRESCRIPTION DM::SHFP))
 (728 306 (:REWRITE DM::INT-CADR-TRIPP))
 (706 706 (:TYPE-PRESCRIPTION DM::VALS))
 (672 336 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (544 16 (:REWRITE |(* (if a b c) x)|))
 (524 268 (:REWRITE DM::SHNFP-SHFP))
 (520 212 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (500 42 (:REWRITE DM::CONSP-NTHCDR))
 (474 12 (:DEFINITION DM::ALL-INTEGERS))
 (459 459 (:REWRITE REDUCE-INTEGERP-+))
 (459 459 (:REWRITE INTEGERP-MINUS-X))
 (459 459 (:META META-INTEGERP-CORRECT))
 (428 24 (:REWRITE DEFAULT-EXPT-2))
 (388 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (356 4 (:DEFINITION DM::NORM-EXPT))
 (315 191 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (288 144 (:REWRITE DM::SPLIT$-CASE-5-2))
 (219 176 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (213 176 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (209 209 (:REWRITE REDUCE-RATIONALP-+))
 (209 209 (:REWRITE REDUCE-RATIONALP-*))
 (209 209 (:REWRITE RATIONALP-MINUS-X))
 (209 209 (:META META-RATIONALP-CORRECT))
 (208 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (208 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (208 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (208 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (208 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (208 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (200 12 (:REWRITE |(+ x (if a b c))|))
 (193 193 (:REWRITE THE-FLOOR-BELOW))
 (193 193 (:REWRITE THE-FLOOR-ABOVE))
 (191 191 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (191 191 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (191 191 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (191 191 (:REWRITE |(equal c (/ x))|))
 (191 191 (:REWRITE |(equal c (- x))|))
 (191 191 (:REWRITE |(equal (/ x) c)|))
 (191 191 (:REWRITE |(equal (/ x) (/ y))|))
 (191 191 (:REWRITE |(equal (- x) c)|))
 (191 191 (:REWRITE |(equal (- x) (- y))|))
 (191 175 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (176 8 (:REWRITE ZIP-OPEN))
 (175 175 (:REWRITE SIMPLIFY-SUMS-<))
 (175 175 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (175 175 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (175 175 (:REWRITE INTEGERP-<-CONSTANT))
 (175 175 (:REWRITE CONSTANT-<-INTEGERP))
 (175 175 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (175 175 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (175 175 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (175 175 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (175 175 (:REWRITE |(< c (- x))|))
 (175 175 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (175 175 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (175 175 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (175 175 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (175 175 (:REWRITE |(< (/ x) (/ y))|))
 (175 175 (:REWRITE |(< (- x) c)|))
 (175 175 (:REWRITE |(< (- x) (- y))|))
 (172 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (172 76 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (168 92 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-7))
 (168 14 (:REWRITE DM::CAR-NTHCDR))
 (160 4 (:REWRITE |(< x (if a b c))|))
 (154 14 (:DEFINITION NTH))
 (151 151 (:REWRITE |(< (* x y) 0)|))
 (150 150 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (150 150 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (150 150 (:REWRITE |(< (/ x) 0)|))
 (144 60 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (144 60 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (128 128 (:TYPE-PRESCRIPTION DM::NORM-EXPT))
 (125 4 (:REWRITE DM::EVALH-NORM-EXPT))
 (116 4 (:REWRITE |(expt 0 n)|))
 (112 56 (:REWRITE DM::INT-CADDR-TRIPP))
 (90 90 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (90 90 (:REWRITE NORMALIZE-ADDENDS))
 (90 1 (:REWRITE |(< (if a b c) x)|))
 (72 44 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (62 62 (:TYPE-PRESCRIPTION DM::NORM-POP))
 (60 60 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (60 60 (:TYPE-PRESCRIPTION EXPT))
 (55 55 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (55 55 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (55 55 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (55 55 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (52 14 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (48 8 (:REWRITE DM::SPLIT$-CASE-5-7))
 (44 44 (:TYPE-PRESCRIPTION DM::NORM-MUL))
 (40 40 (:TYPE-PRESCRIPTION DM::NORM-ADD))
 (40 40 (:REWRITE DM::LEN-VALS))
 (24 12 (:REWRITE DM::SHNFP-INT))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (20 20 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (20 20 (:REWRITE |(< 0 (/ x))|))
 (20 20 (:REWRITE |(< 0 (* x y))|))
 (17 17 (:TYPE-PRESCRIPTION NATP))
 (16 16 (:REWRITE |(expt 1/c n)|))
 (16 16 (:REWRITE |(expt (- x) n)|))
 (12 12 (:REWRITE |(* 1 x)|))
 (10 10 (:TYPE-PRESCRIPTION ABS))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (8 8 (:REWRITE |(* 0 x)|))
 (4 4 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (1 1 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (1 1 (:REWRITE |(* a (/ a) b)|))
 )
(DM::SPLIT$-CASE-3-14
 (162 162 (:DEFINITION MV-NTH))
 )
(DM::SPLIT$-CASE-3
 (100 100 (:DEFINITION MV-NTH))
 )
(DM::SPLIT$-CASE-2-1
 (1571 1008 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (809 809 (:TYPE-PRESCRIPTION DM::ECP))
 (628 227 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (612 374 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (612 374 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (458 458 (:TYPE-PRESCRIPTION DM::TRIPP))
 (377 227 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (186 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (143 85 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (138 3 (:REWRITE ACL2-NUMBERP-X))
 (86 2 (:REWRITE DM::SPLIT$-CASE-5))
 (78 3 (:REWRITE RATIONALP-X))
 (25 25 (:REWRITE DEFAULT-CDR))
 (24 4 (:REWRITE DM::SHNFP-INT))
 (18 2 (:REWRITE DM::SPLIT$-CASE-5-3))
 (12 4 (:REWRITE DM::INTEGERP-EC-X))
 (12 4 (:REWRITE DM::INT-CAR-TRIPP))
 (9 9 (:REWRITE DEFAULT-CAR))
 (8 8 (:TYPE-PRESCRIPTION DM::P-NAT))
 (8 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE DM::P-NAT))
 (6 6 (:REWRITE DM::NATP-Y2))
 (6 6 (:REWRITE DM::NATP-Y1))
 (6 6 (:REWRITE DM::NATP-Y0))
 (6 6 (:REWRITE DM::NATP-X2))
 (6 6 (:REWRITE DM::NATP-X1))
 (6 6 (:REWRITE DM::NATP-X0))
 (6 6 (:REWRITE DM::NATP-P-1/2))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-INTEGERP-CORRECT))
 (6 2 (:REWRITE DM::INT-CADR-TRIPP))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (4 4 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (4 4 (:TYPE-PRESCRIPTION DM::NATP-Y2))
 (4 4 (:TYPE-PRESCRIPTION DM::NATP-Y1))
 (4 4 (:TYPE-PRESCRIPTION DM::NATP-Y0))
 (4 4 (:TYPE-PRESCRIPTION DM::NATP-X2))
 (4 4 (:TYPE-PRESCRIPTION DM::NATP-X1))
 (4 4 (:TYPE-PRESCRIPTION DM::NATP-X0))
 (4 4 (:TYPE-PRESCRIPTION DM::NATP-P-1/2))
 (4 4 (:REWRITE THE-FLOOR-BELOW))
 (4 4 (:REWRITE THE-FLOOR-ABOVE))
 (4 4 (:REWRITE SIMPLIFY-SUMS-<))
 (4 4 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (4 4 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (4 4 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (4 4 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (4 4 (:REWRITE INTEGERP-<-CONSTANT))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-2))
 (4 4 (:REWRITE DEFAULT-LESS-THAN-1))
 (4 4 (:REWRITE CONSTANT-<-INTEGERP))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (4 4 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< c (- x))|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (4 4 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (4 4 (:REWRITE |(< (/ x) (/ y))|))
 (4 4 (:REWRITE |(< (- x) c)|))
 (4 4 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (3 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3 3 (:REWRITE REDUCE-RATIONALP-+))
 (3 3 (:REWRITE REDUCE-RATIONALP-*))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE RATIONALP-MINUS-X))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE |(equal c (/ x))|))
 (3 3 (:REWRITE |(equal c (- x))|))
 (3 3 (:REWRITE |(equal (/ x) c)|))
 (3 3 (:REWRITE |(equal (/ x) (/ y))|))
 (3 3 (:REWRITE |(equal (- x) c)|))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (3 3 (:REWRITE |(< (/ x) 0)|))
 (3 3 (:REWRITE |(< (* x y) 0)|))
 (3 3 (:META META-RATIONALP-CORRECT))
 (2 2 (:REWRITE DM::SHNFP-POW-P))
 (1 1 (:REWRITE DM::SPLIT$-CASE-5-2))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(DM::SPLIT$-CASE-2-2
 (1251 848 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (513 154 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (502 502 (:TYPE-PRESCRIPTION DM::ECP))
 (334 235 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (334 235 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (231 154 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (230 230 (:TYPE-PRESCRIPTION DM::TRIPP))
 (135 81 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (2 1 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-2-2))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(DM::SPLIT$-CASE-2-3
 (2026 1303 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (1100 1100 (:TYPE-PRESCRIPTION DM::ECP))
 (945 546 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (915 546 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (760 2 (:REWRITE DM::SPLIT$-CASE-5))
 (700 700 (:TYPE-PRESCRIPTION DM::TRIPP))
 (459 276 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (455 276 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (325 181 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (212 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (162 4 (:REWRITE |(< x (+ c/d y))|))
 (156 4 (:REWRITE ACL2-NUMBERP-X))
 (88 4 (:REWRITE RATIONALP-X))
 (68 2 (:REWRITE |(< y (+ (- c) x))|))
 (64 64 (:TYPE-PRESCRIPTION DM::P-NAT))
 (56 26 (:REWRITE DEFAULT-LESS-THAN-2))
 (38 22 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (34 34 (:REWRITE DEFAULT-CDR))
 (30 2 (:REWRITE |(* x (+ y z))|))
 (26 26 (:REWRITE THE-FLOOR-BELOW))
 (26 26 (:REWRITE THE-FLOOR-ABOVE))
 (26 26 (:REWRITE DEFAULT-LESS-THAN-1))
 (26 4 (:REWRITE DEFAULT-TIMES-2))
 (24 24 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (24 24 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (24 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (24 8 (:LINEAR DM::P-IS-BIG))
 (22 22 (:REWRITE SIMPLIFY-SUMS-<))
 (22 22 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (22 22 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (22 22 (:REWRITE INTEGERP-<-CONSTANT))
 (22 22 (:REWRITE CONSTANT-<-INTEGERP))
 (22 22 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (22 22 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (22 22 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (22 22 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (22 22 (:REWRITE |(< c (- x))|))
 (22 22 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (22 22 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (22 22 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (22 22 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (22 22 (:REWRITE |(< (/ x) (/ y))|))
 (22 22 (:REWRITE |(< (- x) c)|))
 (22 22 (:REWRITE |(< (- x) (- y))|))
 (18 2 (:REWRITE DM::SPLIT$-CASE-5-3))
 (16 4 (:REWRITE DEFAULT-PLUS-2))
 (15 15 (:REWRITE DEFAULT-CAR))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (12 12 (:TYPE-PRESCRIPTION DM::NATP-Y2))
 (12 12 (:TYPE-PRESCRIPTION DM::NATP-Y1))
 (12 12 (:TYPE-PRESCRIPTION DM::NATP-Y0))
 (12 12 (:TYPE-PRESCRIPTION DM::NATP-X2))
 (12 12 (:TYPE-PRESCRIPTION DM::NATP-X1))
 (12 12 (:TYPE-PRESCRIPTION DM::NATP-X0))
 (12 4 (:REWRITE DM::INTEGERP-EC-X))
 (12 4 (:REWRITE DM::INT-CAR-TRIPP))
 (8 8 (:TYPE-PRESCRIPTION DM::NATP-P-1/2))
 (6 6 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 6 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (6 6 (:REWRITE |(equal c (/ x))|))
 (6 6 (:REWRITE |(equal c (- x))|))
 (6 6 (:REWRITE |(equal (/ x) c)|))
 (6 6 (:REWRITE |(equal (/ x) (/ y))|))
 (6 6 (:REWRITE |(equal (- x) c)|))
 (6 6 (:REWRITE |(equal (- x) (- y))|))
 (6 6 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE DM::SHNFP-INT))
 (4 4 (:REWRITE REDUCE-RATIONALP-+))
 (4 4 (:REWRITE REDUCE-RATIONALP-*))
 (4 4 (:REWRITE RATIONALP-MINUS-X))
 (4 4 (:REWRITE DM::P-NAT))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DM::NATP-Y2))
 (4 4 (:REWRITE DM::NATP-Y1))
 (4 4 (:REWRITE DM::NATP-Y0))
 (4 4 (:REWRITE DM::NATP-X2))
 (4 4 (:REWRITE DM::NATP-X1))
 (4 4 (:REWRITE DM::NATP-X0))
 (4 4 (:REWRITE DM::NATP-P-1/2))
 (4 4 (:REWRITE DEFAULT-TIMES-1))
 (4 4 (:REWRITE DEFAULT-PLUS-1))
 (4 4 (:META META-RATIONALP-CORRECT))
 (4 2 (:REWRITE |(* a (/ a) b)|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:REWRITE DM::SHNFP-POW-P))
 (2 2 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 )
(DM::SPLIT$-CASE-2-4
 (10406 86 (:REWRITE ACL2-NUMBERP-X))
 (7784 86 (:REWRITE RATIONALP-X))
 (5868 144 (:REWRITE DEFAULT-PLUS-1))
 (4608 8 (:REWRITE DM::INTEGERP-EVALH))
 (4568 8 (:DEFINITION DM::SHFP))
 (4146 2121 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (3994 146 (:REWRITE DEFAULT-PLUS-2))
 (3376 14 (:REWRITE |(+ (if a b c) x)|))
 (2854 26 (:REWRITE DEFAULT-TIMES-2))
 (2569 2569 (:TYPE-PRESCRIPTION DM::ECP))
 (1854 462 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-7))
 (1355 10 (:DEFINITION NTHCDR))
 (1226 508 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (1030 1030 (:TYPE-PRESCRIPTION DM::TRIPP))
 (992 508 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (948 212 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (860 10 (:REWRITE |(* (if a b c) x)|))
 (798 10 (:REWRITE DEFAULT-EXPT-2))
 (760 152 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-8))
 (756 26 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (678 349 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (674 349 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (663 3 (:REWRITE DM::EVALH-POW-REWRITE))
 (638 10 (:REWRITE ZP-OPEN))
 (490 80 (:REWRITE DEFAULT-CAR))
 (471 15 (:REWRITE |(+ (+ x y) z)|))
 (470 6 (:REWRITE DEFAULT-EXPT-1))
 (412 4 (:REWRITE DM::CDR-NTHCDR))
 (383 255 (:REWRITE DEFAULT-CDR))
 (296 74 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (256 15 (:REWRITE |(+ y (+ x z))|))
 (236 74 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (236 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (234 129 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (234 24 (:REWRITE DEFAULT-TIMES-1))
 (216 216 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS))
 (216 2 (:REWRITE DM::NTHCDR-CDR))
 (204 4 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (184 8 (:REWRITE |(* 1 x)|))
 (180 30 (:REWRITE DM::SPLIT$-CASE-5-8))
 (170 2 (:REWRITE |(< x (if a b c))|))
 (138 2 (:REWRITE DM::CAR-NTHCDR))
 (136 2 (:DEFINITION NTH))
 (132 22 (:REWRITE DM::SPLIT$-CASE-5-7))
 (126 8 (:REWRITE |(+ 0 x)|))
 (102 42 (:REWRITE DM::INTEGERP-EC-X))
 (102 42 (:REWRITE DM::INT-CAR-TRIPP))
 (98 2 (:REWRITE DM::CONSP-NTHCDR))
 (96 96 (:TYPE-PRESCRIPTION DM::SHFP))
 (85 34 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (84 36 (:REWRITE DM::INT-CADR-TRIPP))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (74 74 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (74 74 (:TYPE-PRESCRIPTION EXPT))
 (69 69 (:REWRITE REDUCE-INTEGERP-+))
 (69 69 (:REWRITE INTEGERP-MINUS-X))
 (69 69 (:META META-INTEGERP-CORRECT))
 (69 36 (:REWRITE DEFAULT-LESS-THAN-2))
 (64 32 (:REWRITE DM::SHNFP-SHFP))
 (63 63 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (63 63 (:REWRITE NORMALIZE-ADDENDS))
 (54 54 (:REWRITE DM::SPLIT$-CASE-2-3))
 (54 36 (:REWRITE DEFAULT-LESS-THAN-1))
 (52 4 (:REWRITE ZIP-OPEN))
 (43 25 (:REWRITE |(+ c (+ d x))|))
 (38 18 (:REWRITE DM::SPLIT$-CASE-2-2))
 (36 36 (:REWRITE THE-FLOOR-BELOW))
 (36 36 (:REWRITE THE-FLOOR-ABOVE))
 (34 34 (:REWRITE SIMPLIFY-SUMS-<))
 (34 34 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (34 34 (:REWRITE REDUCE-RATIONALP-+))
 (34 34 (:REWRITE REDUCE-RATIONALP-*))
 (34 34 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (34 34 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (34 34 (:REWRITE RATIONALP-MINUS-X))
 (34 34 (:REWRITE INTEGERP-<-CONSTANT))
 (34 34 (:REWRITE CONSTANT-<-INTEGERP))
 (34 34 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (34 34 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (34 34 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (34 34 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (34 34 (:REWRITE |(< c (- x))|))
 (34 34 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (34 34 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (34 34 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (34 34 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (34 34 (:REWRITE |(< (/ x) (/ y))|))
 (34 34 (:REWRITE |(< (- x) c)|))
 (34 34 (:REWRITE |(< (- x) (- y))|))
 (34 34 (:META META-RATIONALP-CORRECT))
 (32 16 (:REWRITE DM::SPLIT$-CASE-5-2))
 (28 28 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (28 2 (:REWRITE |(expt 0 n)|))
 (26 26 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (26 26 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (26 26 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (26 26 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (26 26 (:REWRITE |(equal c (/ x))|))
 (26 26 (:REWRITE |(equal c (- x))|))
 (26 26 (:REWRITE |(equal (/ x) c)|))
 (26 26 (:REWRITE |(equal (/ x) (/ y))|))
 (26 26 (:REWRITE |(equal (- x) c)|))
 (26 26 (:REWRITE |(equal (- x) (- y))|))
 (23 23 (:REWRITE FOLD-CONSTS-IN-+))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (17 17 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (17 17 (:REWRITE |(< (/ x) 0)|))
 (17 17 (:REWRITE |(< (* x y) 0)|))
 (16 8 (:REWRITE DM::INT-CADDR-TRIPP))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (11 11 (:REWRITE |(< y (+ (- c) x))|))
 (11 11 (:REWRITE |(< x (+ c/d y))|))
 (11 11 (:REWRITE |(< 0 (/ x))|))
 (11 11 (:REWRITE |(< 0 (* x y))|))
 (6 6 (:REWRITE DM::LEN-VALS))
 (6 6 (:REWRITE |(< (+ c/d x) y)|))
 (6 6 (:REWRITE |(< (+ (- c) x) y)|))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (4 4 (:REWRITE DM::ALL-INTEGERS-VALS))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 (4 4 (:REWRITE |(* 0 x)|))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (1 1 (:REWRITE DM::SHNFP-INT))
 )
(DM::SPLIT$-CASE-2-5
 (46862 402 (:REWRITE ACL2-NUMBERP-X))
 (43618 474 (:REWRITE RATIONALP-X))
 (34398 6 (:DEFINITION DM::EVALH))
 (28248 84 (:REWRITE DM::INTEGERP-EVALH))
 (25729 1 (:DEFINITION DM::SPLIT$))
 (23392 4 (:DEFINITION DM::NORM-ADD))
 (23375 541 (:REWRITE DEFAULT-PLUS-2))
 (23348 44 (:DEFINITION DM::SHFP))
 (17362 8749 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (12529 12529 (:TYPE-PRESCRIPTION DM::ECP))
 (7273 7273 (:TYPE-PRESCRIPTION DM::TRIPP))
 (7230 3398 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (7000 397 (:REWRITE DEFAULT-LESS-THAN-2))
 (6762 3398 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (6470 378 (:REWRITE REDUCE-RATIONALP-*))
 (6118 274 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (5124 2641 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (5094 10 (:REWRITE DM::SPLIT$-CASE-5))
 (5034 727 (:REWRITE DEFAULT-TIMES-1))
 (4992 2513 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (4755 389 (:REWRITE DEFAULT-LESS-THAN-1))
 (4400 40 (:DEFINITION DM::ALL-INTEGERS))
 (4192 48 (:DEFINITION RFIX))
 (3750 378 (:REWRITE REDUCE-RATIONALP-+))
 (3680 32 (:REWRITE DEFAULT-MINUS))
 (3239 61 (:REWRITE ZP-OPEN))
 (3174 46 (:REWRITE DM::CAR-NTHCDR))
 (3150 48 (:DEFINITION NTH))
 (2949 475 (:REWRITE DEFAULT-CAR))
 (2504 30 (:REWRITE |(+ (if a b c) x)|))
 (2323 1452 (:REWRITE DEFAULT-CDR))
 (2120 6 (:REWRITE DM::NTHCDR+))
 (1647 591 (:META META-INTEGERP-CORRECT))
 (1646 6 (:REWRITE DM::EVALH-POW-REWRITE))
 (1539 9 (:DEFINITION NTHCDR))
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 (1506 18 (:REWRITE DEFAULT-EXPT-1))
 (1356 347 (:REWRITE SIMPLIFY-SUMS-<))
 (1174 170 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (894 342 (:REWRITE DM::INTEGERP-EC-X))
 (894 342 (:REWRITE DM::INT-CAR-TRIPP))
 (884 102 (:REWRITE |(< x (+ c/d y))|))
 (858 22 (:REWRITE DEFAULT-EXPT-2))
 (829 33 (:REWRITE |(+ y (+ x z))|))
 (812 8 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (810 274 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (778 8 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (774 404 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (762 298 (:REWRITE DM::INT-CADR-TRIPP))
 (758 347 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (758 8 (:REWRITE MOD-X-Y-=-X . 4))
 (758 8 (:REWRITE MOD-X-Y-=-X . 3))
 (628 8 (:REWRITE MOD-ZERO . 4))
 (622 4 (:DEFINITION DM::NORM-EXPT))
 (614 46 (:REWRITE DM::CONSP-NTHCDR))
 (614 8 (:REWRITE MOD-X-Y-=-X . 2))
 (612 612 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (612 612 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (612 612 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (591 591 (:REWRITE REDUCE-INTEGERP-+))
 (591 591 (:REWRITE INTEGERP-MINUS-X))
 (582 16 (:REWRITE |(+ (+ x y) z)|))
 (568 568 (:TYPE-PRESCRIPTION DM::SHFP))
 (534 8 (:REWRITE MOD-ZERO . 3))
 (499 259 (:REWRITE NORMALIZE-ADDENDS))
 (456 114 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (434 8 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (434 8 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (428 6 (:REWRITE |(< x (if a b c))|))
 (414 92 (:REWRITE |(< y (+ (- c) x))|))
 (397 397 (:REWRITE THE-FLOOR-BELOW))
 (397 397 (:REWRITE THE-FLOOR-ABOVE))
 (392 216 (:REWRITE DM::SHNFP-SHFP))
 (378 378 (:REWRITE RATIONALP-MINUS-X))
 (360 8 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (360 8 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (360 8 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (359 357 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (359 357 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (353 353 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (347 347 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (347 347 (:REWRITE INTEGERP-<-CONSTANT))
 (347 347 (:REWRITE CONSTANT-<-INTEGERP))
 (347 347 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (347 347 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (347 347 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (347 347 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (347 347 (:REWRITE |(< c (- x))|))
 (347 347 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (347 347 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (347 347 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (347 347 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (347 347 (:REWRITE |(< (/ x) (/ y))|))
 (347 347 (:REWRITE |(< (- x) c)|))
 (347 347 (:REWRITE |(< (- x) (- y))|))
 (346 8 (:REWRITE RTL::MOD-DOES-NOTHING))
 (314 274 (:REWRITE |(equal (/ x) c)|))
 (314 274 (:REWRITE |(equal (/ x) (/ y))|))
 (313 313 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (284 142 (:REWRITE DEFAULT-DIVIDE))
 (274 274 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (274 274 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (274 274 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (274 274 (:REWRITE |(equal c (/ x))|))
 (274 274 (:REWRITE |(equal c (- x))|))
 (274 274 (:REWRITE |(equal (- x) c)|))
 (274 274 (:REWRITE |(equal (- x) (- y))|))
 (256 1 (:DEFINITION EVENP))
 (252 12 (:REWRITE ZIP-OPEN))
 (239 239 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (216 152 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (216 152 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (210 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (208 16 (:REWRITE |(* 1 x)|))
 (182 90 (:REWRITE DM::SPLIT$-CASE-2-2))
 (176 88 (:REWRITE DM::SPLIT$-CASE-5-2))
 (176 64 (:LINEAR DM::P-IS-BIG))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (170 170 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (168 152 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (164 30 (:REWRITE DM::SPLIT$-CASE-5-7))
 (164 6 (:REWRITE |(expt 0 n)|))
 (152 152 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (152 152 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (152 152 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (152 152 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (152 152 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (152 152 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (152 152 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (152 152 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (152 152 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (152 152 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (152 152 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (152 152 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (152 152 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (142 142 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (139 87 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (124 124 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (120 40 (:REWRITE |(equal x (/ y))|))
 (114 114 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (114 114 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (114 114 (:TYPE-PRESCRIPTION EXPT))
 (114 114 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (114 114 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (114 114 (:REWRITE |(< (/ x) 0)|))
 (114 114 (:REWRITE |(< (* x y) 0)|))
 (110 10 (:REWRITE BUBBLE-DOWN-+-MATCH-3))
 (104 88 (:REWRITE |(+ c (+ d x))|))
 (104 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (100 100 (:REWRITE DM::LEN-VALS))
 (94 94 (:REWRITE DM::ALL-INTEGERS-VALS))
 (88 44 (:REWRITE DM::INT-CADDR-TRIPP))
 (87 87 (:REWRITE |(< 0 (/ x))|))
 (87 87 (:REWRITE |(< 0 (* x y))|))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (84 84 (:REWRITE |(* c (* d x))|))
 (80 40 (:REWRITE DM::ALL-INTEGERS-NTHCDR))
 (80 40 (:REWRITE |(not (equal x (/ y)))|))
 (76 76 (:REWRITE FOLD-CONSTS-IN-+))
 (64 32 (:REWRITE DEFAULT-MOD-2))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-Y2))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-Y1))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-Y0))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-X2))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-X1))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-X0))
 (40 40 (:TYPE-PRESCRIPTION DM::NATP-P-1/2))
 (32 32 (:REWRITE DM::SPLIT$-CASE-2-3))
 (30 30 (:DEFINITION FIX))
 (26 26 (:REWRITE |(< (+ c/d x) y)|))
 (26 26 (:REWRITE |(< (+ (- c) x) y)|))
 (20 20 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (20 20 (:REWRITE |(+ x (- x))|))
 (20 10 (:REWRITE BUBBLE-DOWN-+-MATCH-1))
 (20 10 (:REWRITE |(* a (/ a) b)|))
 (12 12 (:REWRITE |(expt 1/c n)|))
 (12 12 (:REWRITE |(expt (- x) n)|))
 (10 10 (:REWRITE DM::P-NAT))
 (10 10 (:REWRITE DM::NATP-Y2))
 (10 10 (:REWRITE DM::NATP-Y1))
 (10 10 (:REWRITE DM::NATP-Y0))
 (10 10 (:REWRITE DM::NATP-X2))
 (10 10 (:REWRITE DM::NATP-X1))
 (10 10 (:REWRITE DM::NATP-X0))
 (10 10 (:REWRITE DM::NATP-P-1/2))
 (9 3 (:REWRITE DM::SHNFP-INT))
 (8 8 (:TYPE-PRESCRIPTION DM::NORM-POP))
 (8 8 (:TYPE-PRESCRIPTION DM::NORM-MUL))
 (8 8 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (8 8 (:REWRITE INTEGERP-/))
 (8 8 (:REWRITE |(mod x (- y))| . 3))
 (8 8 (:REWRITE |(mod x (- y))| . 2))
 (8 8 (:REWRITE |(mod x (- y))| . 1))
 (8 8 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (8 8 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (6 6 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 (4 4 (:TYPE-PRESCRIPTION ABS))
 (4 4 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (4 4 (:REWRITE |(< (* x y) 0) rationalp (* x y)|))
 (3 3 (:REWRITE |(equal (+ (- c) x) y)|))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 3))
 (2 2 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (2 2 (:REWRITE |(equal (* x y) 0)|))
 )
(DM::SPLIT$-CASE-2-6
 (7185 23 (:REWRITE ACL2-NUMBERP-X))
 (6872 23 (:REWRITE RATIONALP-X))
 (6336 12 (:REWRITE DM::INTEGERP-EVALH))
 (6276 12 (:DEFINITION DM::SHFP))
 (5213 81 (:REWRITE DEFAULT-PLUS-2))
 (2768 1384 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (2074 18 (:REWRITE DEFAULT-TIMES-2))
 (1873 1873 (:TYPE-PRESCRIPTION DM::ECP))
 (891 439 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (878 439 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (831 831 (:TYPE-PRESCRIPTION DM::TRIPP))
 (625 6 (:DEFINITION NTHCDR))
 (522 35 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (518 6 (:REWRITE DEFAULT-EXPT-1))
 (512 286 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (461 345 (:REWRITE DEFAULT-CDR))
 (444 222 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (424 101 (:REWRITE DEFAULT-CAR))
 (360 78 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS-INTEGER))
 (360 8 (:REWRITE ZP-OPEN))
 (346 77 (:REWRITE DEFAULT-PLUS-1))
 (262 8 (:REWRITE |(+ (if a b c) x)|))
 (261 7 (:REWRITE |(+ (+ x y) z)|))
 (204 4 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (199 4 (:REWRITE DM::EVALH-POW-REWRITE))
 (190 9 (:REWRITE |(+ y (+ x z))|))
 (176 6 (:REWRITE |(* (if a b c) x)|))
 (172 16 (:REWRITE DEFAULT-TIMES-1))
 (144 144 (:TYPE-PRESCRIPTION DM::SHFP))
 (144 72 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (138 2 (:REWRITE DM::CAR-NTHCDR))
 (136 2 (:DEFINITION NTH))
 (112 28 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-7))
 (100 4 (:REWRITE ZIP-OPEN))
 (98 2 (:REWRITE DM::CONSP-NTHCDR))
 (96 48 (:REWRITE DM::SHNFP-SHFP))
 (93 43 (:REWRITE DM::INTEGERP-EC-X))
 (93 43 (:REWRITE DM::INT-CAR-TRIPP))
 (87 42 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (82 82 (:TYPE-PRESCRIPTION DM::ALL-INTEGERS))
 (72 36 (:REWRITE DM::INT-CADR-TRIPP))
 (69 42 (:REWRITE DEFAULT-LESS-THAN-2))
 (68 2 (:REWRITE |(expt 0 n)|))
 (62 62 (:REWRITE REDUCE-INTEGERP-+))
 (62 62 (:REWRITE INTEGERP-MINUS-X))
 (62 62 (:META META-INTEGERP-CORRECT))
 (60 42 (:REWRITE DEFAULT-LESS-THAN-1))
 (60 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (48 24 (:REWRITE DM::SPLIT$-CASE-5-2))
 (48 24 (:REWRITE DM::SPLIT$-CASE-2-2))
 (48 12 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (48 12 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (48 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (48 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (42 42 (:REWRITE THE-FLOOR-BELOW))
 (42 42 (:REWRITE THE-FLOOR-ABOVE))
 (42 42 (:REWRITE SIMPLIFY-SUMS-<))
 (42 42 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (42 42 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (42 42 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (42 42 (:REWRITE INTEGERP-<-CONSTANT))
 (42 42 (:REWRITE CONSTANT-<-INTEGERP))
 (42 42 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (42 42 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (42 42 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (42 42 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (42 42 (:REWRITE |(< c (- x))|))
 (42 42 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (42 42 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (42 42 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (42 42 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (42 42 (:REWRITE |(< (/ x) (/ y))|))
 (42 42 (:REWRITE |(< (- x) c)|))
 (42 42 (:REWRITE |(< (- x) (- y))|))
 (36 36 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (35 35 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (35 35 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (35 35 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (35 35 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (35 35 (:REWRITE NORMALIZE-ADDENDS))
 (35 35 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (35 35 (:REWRITE |(equal c (/ x))|))
 (35 35 (:REWRITE |(equal c (- x))|))
 (35 35 (:REWRITE |(equal (/ x) c)|))
 (35 35 (:REWRITE |(equal (/ x) (/ y))|))
 (35 35 (:REWRITE |(equal (- x) c)|))
 (35 35 (:REWRITE |(equal (- x) (- y))|))
 (30 6 (:REWRITE DEFAULT-EXPT-2))
 (29 29 (:TYPE-PRESCRIPTION DM::NORM-POP))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (26 26 (:REWRITE |(< (/ x) 0)|))
 (26 26 (:REWRITE |(< (* x y) 0)|))
 (24 12 (:REWRITE DM::INT-CADDR-TRIPP))
 (23 23 (:REWRITE REDUCE-RATIONALP-+))
 (23 23 (:REWRITE REDUCE-RATIONALP-*))
 (23 23 (:REWRITE RATIONALP-MINUS-X))
 (23 23 (:META META-RATIONALP-CORRECT))
 (13 13 (:REWRITE FOLD-CONSTS-IN-+))
 (13 13 (:REWRITE |(+ c (+ d x))|))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (12 12 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (12 12 (:TYPE-PRESCRIPTION EXPT))
 (12 4 (:REWRITE |(* 1 x)|))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (7 7 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (7 7 (:REWRITE |(< y (+ (- c) x))|))
 (7 7 (:REWRITE |(< x (+ c/d y))|))
 (7 7 (:REWRITE |(< 0 (/ x))|))
 (7 7 (:REWRITE |(< 0 (* x y))|))
 (6 6 (:REWRITE DM::LEN-VALS))
 (6 6 (:REWRITE |(< (+ c/d x) y)|))
 (6 6 (:REWRITE |(< (+ (- c) x) y)|))
 (6 6 (:REWRITE |(+ 0 x)|))
 (5 2 (:REWRITE DM::SHNFP-INT))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (4 4 (:REWRITE DM::ALL-INTEGERS-VALS))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 (4 4 (:REWRITE |(* 0 x)|))
 (2 2 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 )
(DM::SPLIT$-CASE-2-7
 (45 45 (:DEFINITION MV-NTH))
 (4 4 (:TYPE-PRESCRIPTION DM::TRIPP))
 (4 4 (:TYPE-PRESCRIPTION DM::SHNFP))
 (4 4 (:TYPE-PRESCRIPTION DM::ECP))
 (4 2 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (4 2 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-2-2))
 (4 2 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (4 2 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (4 2 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (4 2 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 )
(DM::SPLIT$-CASE-2-8
 (46784 8 (:DEFINITION DM::NORM-ADD))
 (29729 379 (:REWRITE ACL2-NUMBERP-X))
 (16214 359 (:REWRITE RATIONALP-X))
 (12434 124 (:REWRITE DEFAULT-LESS-THAN-2))
 (9880 4940 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (9488 240 (:REWRITE DEFAULT-PLUS-1))
 (9213 9213 (:TYPE-PRESCRIPTION DM::ECP))
 (8636 108 (:REWRITE DEFAULT-LESS-THAN-1))
 (7879 7879 (:TYPE-PRESCRIPTION DM::TRIPP))
 (7360 64 (:REWRITE DEFAULT-MINUS))
 (7110 3555 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (7110 3555 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (6718 85 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (5897 2946 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (5892 2946 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (5518 260 (:REWRITE DEFAULT-PLUS-2))
 (2880 206 (:REWRITE DEFAULT-CAR))
 (1300 38 (:REWRITE DEFAULT-TIMES-1))
 (1278 316 (:REWRITE DEFAULT-CDR))
 (1244 8 (:DEFINITION DM::NORM-EXPT))
 (1077 359 (:REWRITE DM::INTEGERP-EC-X))
 (1077 359 (:REWRITE DM::INT-CAR-TRIPP))
 (924 308 (:REWRITE DM::INT-CADR-TRIPP))
 (884 40 (:REWRITE |(+ x (if a b c))|))
 (677 85 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (516 8 (:REWRITE |(< x (if a b c))|))
 (512 2 (:DEFINITION EVENP))
 (369 369 (:REWRITE REDUCE-INTEGERP-+))
 (369 369 (:REWRITE INTEGERP-MINUS-X))
 (369 369 (:META META-INTEGERP-CORRECT))
 (359 359 (:REWRITE REDUCE-RATIONALP-+))
 (359 359 (:REWRITE REDUCE-RATIONALP-*))
 (359 359 (:REWRITE RATIONALP-MINUS-X))
 (359 359 (:META META-RATIONALP-CORRECT))
 (132 28 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (124 124 (:REWRITE THE-FLOOR-BELOW))
 (124 124 (:REWRITE THE-FLOOR-ABOVE))
 (124 4 (:REWRITE |(* (if a b c) x)|))
 (101 66 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (96 96 (:TYPE-PRESCRIPTION DM::NORM-POP))
 (88 44 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (88 10 (:REWRITE |(* y x)|))
 (85 85 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (85 85 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (85 85 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (85 85 (:REWRITE |(equal c (/ x))|))
 (85 85 (:REWRITE |(equal c (- x))|))
 (85 85 (:REWRITE |(equal (/ x) c)|))
 (85 85 (:REWRITE |(equal (/ x) (/ y))|))
 (85 85 (:REWRITE |(equal (- x) c)|))
 (85 85 (:REWRITE |(equal (- x) (- y))|))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (76 76 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (75 75 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (75 75 (:REWRITE NORMALIZE-ADDENDS))
 (72 68 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (72 68 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (72 6 (:REWRITE |(* x (+ y z))|))
 (68 68 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (68 68 (:REWRITE INTEGERP-<-CONSTANT))
 (68 68 (:REWRITE CONSTANT-<-INTEGERP))
 (68 68 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (68 68 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (68 68 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (68 68 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (68 68 (:REWRITE |(< c (- x))|))
 (68 68 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (68 68 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (68 68 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (68 68 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (68 68 (:REWRITE |(< (/ x) (/ y))|))
 (68 68 (:REWRITE |(< (- x) c)|))
 (68 68 (:REWRITE |(< (- x) (- y))|))
 (66 66 (:REWRITE SIMPLIFY-SUMS-<))
 (40 8 (:REWRITE |(+ c (+ d x))|))
 (38 38 (:REWRITE DEFAULT-TIMES-2))
 (32 32 (:REWRITE |(+ 0 x)|))
 (28 28 (:REWRITE |(< 0 (/ x))|))
 (28 28 (:REWRITE |(< 0 (* x y))|))
 (28 2 (:REWRITE |(+ y (+ x z))|))
 (26 26 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (18 18 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (18 18 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (18 18 (:REWRITE |(< (/ x) 0)|))
 (18 18 (:REWRITE |(< (* x y) 0)|))
 (16 16 (:TYPE-PRESCRIPTION DM::NORM-MUL))
 (10 4 (:REWRITE DM::SHNFP-INT))
 (8 8 (:TYPE-PRESCRIPTION ABS))
 (8 8 (:REWRITE |(< y (+ (- c) x))|))
 (8 8 (:REWRITE |(< x (+ c/d y))|))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE |(< 0 (* x y)) rationalp (* x y)|))
 (2 2 (:REWRITE |(equal (+ (- c) x) y)|))
 )
(DM::SPLIT$-CASE-2
 (52 52 (:DEFINITION MV-NTH))
 (4 4 (:TYPE-PRESCRIPTION DM::TRIPP))
 (4 4 (:TYPE-PRESCRIPTION DM::ECP))
 (4 2 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (4 2 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-2-2))
 (4 2 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (4 2 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (4 2 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (4 2 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 )
(DM::SPLIT$-LEMMA
 (117344 20 (:DEFINITION DM::NORM-ADD))
 (92921 1055 (:REWRITE ACL2-NUMBERP-X))
 (60307 1064 (:REWRITE RATIONALP-X))
 (31495 548 (:REWRITE DEFAULT-LESS-THAN-2))
 (29174 14587 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (26678 834 (:REWRITE DEFAULT-PLUS-2))
 (26400 26400 (:TYPE-PRESCRIPTION DM::ECP))
 (21852 508 (:REWRITE DEFAULT-LESS-THAN-1))
 (21288 21288 (:TYPE-PRESCRIPTION DM::TRIPP))
 (19848 9925 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (19848 9925 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (18405 394 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (18400 160 (:REWRITE DEFAULT-MINUS))
 (17142 61 (:REWRITE DM::INTEGERP-EVALH))
 (16895 7815 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (15920 7900 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-2-2))
 (15690 30 (:DEFINITION DM::SHFP))
 (15310 7655 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (8508 759 (:REWRITE DEFAULT-CAR))
 (6215 621 (:REWRITE DEFAULT-TIMES-1))
 (4456 1679 (:REWRITE DEFAULT-CDR))
 (3586 10 (:REWRITE DM::SPLIT$-CASE-5))
 (3389 1023 (:REWRITE REDUCE-RATIONALP-*))
 (3320 20 (:DEFINITION DM::NORM-EXPT))
 (2880 990 (:REWRITE DM::INTEGERP-EC-X))
 (2880 990 (:REWRITE DM::INT-CAR-TRIPP))
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 (2109 1023 (:REWRITE REDUCE-RATIONALP-+))
 (1450 5 (:DEFINITION EVENP))
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 (1330 20 (:REWRITE |(< x (if a b c))|))
 (1291 1023 (:META META-RATIONALP-CORRECT))
 (1204 1204 (:REWRITE REDUCE-INTEGERP-+))
 (1204 1204 (:REWRITE INTEGERP-MINUS-X))
 (1085 31 (:DEFINITION DM::ALL-INTEGERS))
 (1023 1023 (:REWRITE RATIONALP-MINUS-X))
 (864 40 (:DEFINITION RFIX))
 (825 15 (:REWRITE DEFAULT-EXPT-1))
 (823 41 (:REWRITE |(< x (+ c/d y))|))
 (612 8 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (603 104 (:REWRITE DM::ALL-INTEGERS-INTEGER))
 (602 602 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (602 602 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (602 602 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (583 8 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (569 14 (:DEFINITION NTHCDR))
 (557 8 (:REWRITE MOD-X-Y-=-X . 4))
 (557 8 (:REWRITE MOD-X-Y-=-X . 3))
 (555 5 (:REWRITE DM::NTHCDR+))
 (548 548 (:REWRITE THE-FLOOR-BELOW))
 (548 548 (:REWRITE THE-FLOOR-ABOVE))
 (545 388 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (463 8 (:REWRITE MOD-X-Y-=-X . 2))
 (460 20 (:REWRITE |(+ (if a b c) x)|))
 (432 36 (:REWRITE DM::CAR-NTHCDR))
 (430 394 (:REWRITE |(equal (/ x) c)|))
 (430 394 (:REWRITE |(equal (/ x) (/ y))|))
 (429 39 (:DEFINITION NTH))
 (428 8 (:REWRITE MOD-ZERO . 4))
 (416 388 (:REWRITE SIMPLIFY-SUMS-<))
 (408 398 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (408 398 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (394 394 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (394 394 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (394 394 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (394 394 (:REWRITE |(equal c (/ x))|))
 (394 394 (:REWRITE |(equal c (- x))|))
 (394 394 (:REWRITE |(equal (- x) c)|))
 (394 394 (:REWRITE |(equal (- x) (- y))|))
 (392 392 (:TYPE-PRESCRIPTION DM::SHFP))
 (388 388 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (388 388 (:REWRITE INTEGERP-<-CONSTANT))
 (388 388 (:REWRITE CONSTANT-<-INTEGERP))
 (388 388 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (388 388 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
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 (388 388 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (388 388 (:REWRITE |(< c (- x))|))
 (388 388 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (388 388 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (388 388 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (388 388 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (388 388 (:REWRITE |(< (/ x) (/ y))|))
 (388 388 (:REWRITE |(< (- x) c)|))
 (388 388 (:REWRITE |(< (- x) (- y))|))
 (369 8 (:REWRITE MOD-ZERO . 3))
 (360 180 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (357 357 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (353 31 (:REWRITE |(< y (+ (- c) x))|))
 (341 9 (:REWRITE DM::EVALH-POW-REWRITE))
 (338 78 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (300 300 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (300 300 (:REWRITE NORMALIZE-ADDENDS))
 (291 8 (:REWRITE RTL::MOD-DOES-NOTHING))
 (290 290 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (289 8 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (289 8 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (278 139 (:REWRITE DEFAULT-DIVIDE))
 (272 152 (:REWRITE DM::SHNFP-SHFP))
 (260 164 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (260 164 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (250 10 (:REWRITE ZIP-OPEN))
 (248 8 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (248 8 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (248 8 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (192 36 (:REWRITE DM::CONSP-NTHCDR))
 (188 164 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (177 177 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (177 177 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (177 177 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (176 64 (:LINEAR DM::P-IS-BIG))
 (170 5 (:REWRITE |(expt 0 n)|))
 (165 5 (:REWRITE |(+ (+ x y) z)|))
 (164 164 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (164 164 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (164 164 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (164 164 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (164 164 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (164 164 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (164 164 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (164 164 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (164 164 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (164 164 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (164 164 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (164 164 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (164 164 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (150 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (144 72 (:TYPE-PRESCRIPTION TRUE-LISTP-NTHCDR-TYPE-PRESCRIPTION))
 (139 139 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (130 130 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (130 130 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (130 130 (:REWRITE |(< (/ x) 0)|))
 (130 130 (:REWRITE |(< (* x y) 0)|))
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 (95 15 (:REWRITE |(+ c (+ d x))|))
 (87 1 (:REWRITE DM::SHFP-POP-POW-ATOM))
 (78 78 (:REWRITE |(< 0 (/ x))|))
 (78 78 (:REWRITE |(< 0 (* x y))|))
 (75 15 (:REWRITE DEFAULT-EXPT-2))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (72 36 (:REWRITE |(not (equal x (/ y)))|))
 (70 70 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-7))
 (70 5 (:REWRITE |(+ y (+ x z))|))
 (64 32 (:REWRITE DEFAULT-MOD-2))
 (62 31 (:REWRITE DM::ALL-INTEGERS-NTHCDR))
 (60 60 (:REWRITE DM::LEN-VALS))
 (60 30 (:REWRITE DM::INT-CADDR-TRIPP))
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 (55 55 (:REWRITE DM::ALL-INTEGERS-VALS))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-Y2))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-Y1))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-Y0))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-X2))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-X1))
 (52 52 (:TYPE-PRESCRIPTION DM::NATP-X0))
 (52 1 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 1))
 (42 42 (:REWRITE |(* c (* d x))|))
 (40 40 (:TYPE-PRESCRIPTION DM::NORM-POP))
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 (40 40 (:TYPE-PRESCRIPTION DM::NATP-P-1/2))
 (30 30 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-6))
 (30 30 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-RATIONALP-BASE))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (30 30 (:TYPE-PRESCRIPTION EXPT))
 (24 24 (:TYPE-PRESCRIPTION NATP))
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 (8 8 (:REWRITE |(mod x (- y))| . 3))
 (8 8 (:REWRITE |(mod x (- y))| . 2))
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 (8 8 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (8 8 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (5 5 (:REWRITE FOLD-CONSTS-IN-+))
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 (4 4 (:REWRITE |(< (+ c/d x) y)|))
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 (1 1 (:REWRITE |(mod (+ x y) z) where (<= z 0)| . 2))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(equal (* x y) 0)|))
 )
(DM::REWRITE$)
(DM::EVALH$-NORM-VAR
 (9 6 (:REWRITE DEFAULT-TIMES-2))
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 (9 6 (:REWRITE DEFAULT-PLUS-2))
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 (3 3 (:REWRITE DEFAULT-EXPT-2))
 (3 3 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE |(expt 1/c n)|))
 (3 3 (:REWRITE |(expt (- x) n)|))
 (2 2 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (2 2 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 )
(DM::REWRITE$-LEMMA
 (289856 56 (:DEFINITION DM::NORM-ADD))
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 (330 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (330 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (330 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (330 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
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 (330 330 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
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 (20 20 (:TYPE-PRESCRIPTION INTP-*))
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 )
(DM::REDUCE$)
(DM::POLYP$)
(DM::EVALH$-EVALP$
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 (6422 2 (:DEFINITION DM::EVALP))
 (4934 4934 (:TYPE-PRESCRIPTION DM::ECP))
 (4738 14 (:DEFINITION ASSOC-EQUAL))
 (4476 179 (:REWRITE RATIONALP-X))
 (4140 175 (:REWRITE DEFAULT-CAR))
 (3843 349 (:REWRITE DEFAULT-CDR))
 (3094 26 (:REWRITE DEFAULT-LESS-THAN-2))
 (3051 82 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2352 64 (:REWRITE DEFAULT-PLUS-1))
 (2203 1091 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (2195 2195 (:TYPE-PRESCRIPTION DM::TRIPP))
 (2182 1091 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (2154 22 (:REWRITE DEFAULT-LESS-THAN-1))
 (1978 28 (:REWRITE DEFAULT-MINUS))
 (1620 707 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-2-2))
 (1418 1418 (:TYPE-PRESCRIPTION DM::SHNFP))
 (1414 707 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (1414 707 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (1285 70 (:REWRITE DEFAULT-PLUS-2))
 (1078 1078 (:TYPE-PRESCRIPTION DM::VALS))
 (801 1 (:DEFINITION DM::POLYP))
 (578 2 (:DEFINITION DM::NORM-NEG))
 (321 107 (:REWRITE DM::INTEGERP-EC-X))
 (321 107 (:REWRITE DM::INT-CAR-TRIPP))
 (236 6 (:DEFINITION MEMBER-EQUAL))
 (230 82 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (219 73 (:REWRITE DM::INT-CADR-TRIPP))
 (218 10 (:REWRITE |(+ x (if a b c))|))
 (179 179 (:REWRITE REDUCE-RATIONALP-+))
 (179 179 (:REWRITE REDUCE-RATIONALP-*))
 (179 179 (:REWRITE RATIONALP-MINUS-X))
 (179 179 (:META META-RATIONALP-CORRECT))
 (154 154 (:REWRITE REDUCE-INTEGERP-+))
 (154 154 (:REWRITE INTEGERP-MINUS-X))
 (154 154 (:META META-INTEGERP-CORRECT))
 (104 1 (:REWRITE DM::EVALH-POW-REWRITE))
 (94 1 (:DEFINITION EQL))
 (88 6 (:REWRITE DEFAULT-EXPT-2))
 (84 6 (:REWRITE DEFAULT-TIMES-2))
 (82 82 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (82 82 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (82 82 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (82 82 (:REWRITE |(equal c (/ x))|))
 (82 82 (:REWRITE |(equal c (- x))|))
 (82 82 (:REWRITE |(equal (/ x) c)|))
 (82 82 (:REWRITE |(equal (/ x) (/ y))|))
 (82 82 (:REWRITE |(equal (- x) c)|))
 (82 82 (:REWRITE |(equal (- x) (- y))|))
 (76 1 (:DEFINITION NATP))
 (72 4 (:REWRITE DEFAULT-EXPT-1))
 (70 35 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (60 14 (:REWRITE |(+ y x)|))
 (55 55 (:TYPE-PRESCRIPTION DM::NORM))
 (44 4 (:REWRITE DEFAULT-TIMES-1))
 (42 1 (:DEFINITION DM::NORM-EXPT))
 (36 36 (:REWRITE CAR-CONS))
 (35 1 (:REWRITE ZP-OPEN))
 (26 26 (:REWRITE THE-FLOOR-BELOW))
 (26 26 (:REWRITE THE-FLOOR-ABOVE))
 (26 2 (:REWRITE ZIP-OPEN))
 (24 12 (:REWRITE DM::MEMBER-LEN-POS))
 (18 18 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (18 18 (:REWRITE NORMALIZE-ADDENDS))
 (18 2 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (16 1 (:DEFINITION TRUE-LISTP))
 (14 14 (:REWRITE SIMPLIFY-SUMS-<))
 (14 14 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (14 14 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (14 14 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (14 14 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (14 14 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (14 14 (:REWRITE INTEGERP-<-CONSTANT))
 (14 14 (:REWRITE CONSTANT-<-INTEGERP))
 (14 14 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (14 14 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (14 14 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (14 14 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (14 14 (:REWRITE |(< c (- x))|))
 (14 14 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (14 14 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (14 14 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (14 14 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (14 14 (:REWRITE |(< (/ x) (/ y))|))
 (14 14 (:REWRITE |(< (- x) c)|))
 (14 14 (:REWRITE |(< (- x) (- y))|))
 (12 12 (:REWRITE CDR-CONS))
 (11 11 (:REWRITE DM::PERM-MEMBER))
 (10 10 (:REWRITE |(+ 0 x)|))
 (7 1 (:DEFINITION LEN))
 (6 2 (:REWRITE DM::SHNFP-INT))
 (6 1 (:REWRITE DM::SPLIT$-CASE-5-2))
 (6 1 (:REWRITE DM::SPLIT$-CASE-2-2))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (5 5 (:REWRITE |(< 0 (/ x))|))
 (5 5 (:REWRITE |(< 0 (* x y))|))
 (5 5 (:REWRITE |(< (/ x) 0)|))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (4 2 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (3 1 (:REWRITE DM::INT-CADDR-TRIPP))
 (2 2 (:TYPE-PRESCRIPTION DM::NORM-NEG))
 (2 2 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (2 2 (:REWRITE SET::IN-SET))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 )
(DM::SHNFP-NORM-POLYP)
(DM::REDUCE$-CORRECT
 (25000 2 (:DEFINITION DM::NORM))
 (23152 4 (:DEFINITION DM::NORM-ADD))
 (15680 264 (:REWRITE ACL2-NUMBERP-X))
 (8616 259 (:REWRITE RATIONALP-X))
 (6202 62 (:REWRITE DEFAULT-LESS-THAN-2))
 (5116 106 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4789 4789 (:TYPE-PRESCRIPTION DM::ECP))
 (4764 2381 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-Y))
 (4596 116 (:REWRITE DEFAULT-PLUS-1))
 (4318 54 (:REWRITE DEFAULT-LESS-THAN-1))
 (4048 4048 (:TYPE-PRESCRIPTION DM::TRIPP))
 (4012 2000 (:TYPE-PRESCRIPTION DM::INT-CAR-TRIPP))
 (4000 2000 (:TYPE-PRESCRIPTION DM::INTEGERP-EC-X))
 (3860 48 (:REWRITE DEFAULT-MINUS))
 (2672 1336 (:TYPE-PRESCRIPTION DM::SPLIT$-CASE-5-2))
 (2672 1336 (:TYPE-PRESCRIPTION DM::INT-CADR-TRIPP))
 (2460 126 (:REWRITE DEFAULT-PLUS-2))
 (1600 146 (:REWRITE DEFAULT-CAR))
 (1218 2 (:DEFINITION DM::EVALP))
 (1092 4 (:DEFINITION DM::NORM-NEG))
 (803 220 (:REWRITE DEFAULT-CDR))
 (612 204 (:REWRITE DM::INTEGERP-EC-X))
 (612 204 (:REWRITE DM::INT-CAR-TRIPP))
 (579 259 (:REWRITE REDUCE-RATIONALP-*))
 (438 146 (:REWRITE DM::INT-CADR-TRIPP))
 (414 18 (:REWRITE |(+ x (if a b c))|))
 (406 106 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (271 271 (:REWRITE REDUCE-INTEGERP-+))
 (271 271 (:REWRITE INTEGERP-MINUS-X))
 (271 271 (:META META-INTEGERP-CORRECT))
 (259 259 (:REWRITE REDUCE-RATIONALP-+))
 (259 259 (:REWRITE RATIONALP-MINUS-X))
 (259 259 (:META META-RATIONALP-CORRECT))
 (174 66 (:REWRITE DEFAULT-TIMES-2))
 (134 64 (:REWRITE DEFAULT-TIMES-1))
 (122 2 (:DEFINITION ASSOC-EQUAL))
 (114 106 (:REWRITE |(equal (/ x) c)|))
 (114 106 (:REWRITE |(equal (/ x) (/ y))|))
 (112 26 (:REWRITE |(+ y x)|))
 (108 2 (:DEFINITION MEMBER-EQUAL))
 (106 106 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (106 106 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (106 106 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (106 106 (:REWRITE |(equal c (/ x))|))
 (106 106 (:REWRITE |(equal c (- x))|))
 (106 106 (:REWRITE |(equal (- x) c)|))
 (106 106 (:REWRITE |(equal (- x) (- y))|))
 (104 2 (:REWRITE MOD-X-Y-=-X-Y . 2))
 (98 2 (:REWRITE MOD-X-Y-=-X+Y . 2))
 (90 2 (:REWRITE MOD-X-Y-=-X . 4))
 (90 2 (:REWRITE MOD-X-Y-=-X . 3))
 (88 6 (:REWRITE DEFAULT-EXPT-2))
 (84 2 (:DEFINITION DM::NORM-EXPT))
 (78 2 (:REWRITE MOD-X-Y-=-X . 2))
 (72 4 (:REWRITE DEFAULT-EXPT-1))
 (70 14 (:TYPE-PRESCRIPTION MOD-ZERO . 2))
 (70 14 (:TYPE-PRESCRIPTION MOD-ZERO . 1))
 (70 2 (:REWRITE ZP-OPEN))
 (64 64 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (64 64 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (64 64 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (64 2 (:REWRITE DM::MEMBER-LEN-POS))
 (62 62 (:REWRITE THE-FLOOR-BELOW))
 (62 62 (:REWRITE THE-FLOOR-ABOVE))
 (60 30 (:REWRITE DEFAULT-DIVIDE))
 (60 2 (:REWRITE RTL::MOD-DOES-NOTHING))
 (58 2 (:REWRITE MOD-ZERO . 4))
 (52 2 (:REWRITE MOD-ZERO . 3))
 (48 48 (:TYPE-PRESCRIPTION DM::NORM))
 (44 8 (:DEFINITION RFIX))
 (42 38 (:REWRITE SIMPLIFY-SUMS-<))
 (42 38 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (39 2 (:DEFINITION TRUE-LISTP))
 (38 38 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (38 38 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (38 38 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (38 38 (:REWRITE INTEGERP-<-CONSTANT))
 (38 38 (:REWRITE CONSTANT-<-INTEGERP))
 (38 38 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (38 38 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (38 38 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (38 38 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (38 38 (:REWRITE |(< c (- x))|))
 (38 38 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (38 38 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (38 38 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (38 38 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (38 38 (:REWRITE |(< (/ x) (/ y))|))
 (38 38 (:REWRITE |(< (- x) c)|))
 (38 38 (:REWRITE |(< (- x) (- y))|))
 (38 2 (:DEFINITION =))
 (36 4 (:REWRITE SET::SETS-ARE-TRUE-LISTS-CHEAP))
 (36 4 (:DEFINITION LEN))
 (36 2 (:REWRITE MOD-X-Y-=-X-Y . 3))
 (36 2 (:REWRITE MOD-X-Y-=-X+Y . 3))
 (34 34 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (34 34 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (34 34 (:REWRITE NORMALIZE-ADDENDS))
 (34 2 (:REWRITE MOD-CANCEL-*-REWRITING-GOAL-LITERAL))
 (34 2 (:REWRITE |(mod x (* y (/ z))) rewriting-goal-literal|))
 (34 2 (:REWRITE |(mod (* x (/ y)) z) rewriting-goal-literal|))
 (32 32 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (30 30 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (28 14 (:TYPE-PRESCRIPTION RTL::NATP-MOD))
 (26 2 (:REWRITE ZIP-OPEN))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (24 8 (:REWRITE |(equal x (/ y))|))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (22 22 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (18 18 (:REWRITE |(+ 0 x)|))
 (16 8 (:TYPE-PRESCRIPTION DM::INT-CADDR-TRIPP))
 (16 8 (:REWRITE |(not (equal x (/ y)))|))
 (15 15 (:TYPE-PRESCRIPTION DM::VARS))
 (14 14 (:TYPE-PRESCRIPTION RTL::RATIONALP-MOD))
 (14 14 (:TYPE-PRESCRIPTION RATIONALP-MOD))
 (14 14 (:TYPE-PRESCRIPTION RTL::NATP-MOD-2))
 (14 14 (:TYPE-PRESCRIPTION NATP))
 (14 14 (:TYPE-PRESCRIPTION MOD-ZERO . 3))
 (14 14 (:TYPE-PRESCRIPTION MOD-POSITIVE . 2))
 (14 14 (:TYPE-PRESCRIPTION MOD-POSITIVE . 1))
 (14 14 (:TYPE-PRESCRIPTION MOD-NONPOSITIVE))
 (14 14 (:TYPE-PRESCRIPTION MOD-NONNEGATIVE))
 (14 14 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 2))
 (14 14 (:TYPE-PRESCRIPTION MOD-NEGATIVE . 1))
 (14 14 (:TYPE-PRESCRIPTION INTEGERP-MOD-2))
 (14 14 (:TYPE-PRESCRIPTION INTEGERP-MOD-1))
 (14 14 (:TYPE-PRESCRIPTION RTL::INTEGERP-MOD))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (14 14 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (14 14 (:REWRITE |(< (/ x) 0)|))
 (14 14 (:REWRITE |(< (* x y) 0)|))
 (14 6 (:LINEAR DM::P-IS-BIG))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (12 12 (:REWRITE |(< 0 (/ x))|))
 (12 12 (:REWRITE |(< 0 (* x y))|))
 (12 6 (:REWRITE DEFAULT-MOD-2))
 (12 4 (:REWRITE DM::SHNFP-INT))
 (12 2 (:REWRITE DM::SPLIT$-CASE-5-2))
 (12 2 (:REWRITE DM::SPLIT$-CASE-2-2))
 (8 8 (:TYPE-PRESCRIPTION SET::SETP-TYPE))
 (8 4 (:REWRITE SET::NONEMPTY-MEANS-SET))
 (6 2 (:REWRITE DM::INT-CADDR-TRIPP))
 (4 4 (:TYPE-PRESCRIPTION DM::VLIST))
 (4 4 (:TYPE-PRESCRIPTION DM::NORM-NEG))
 (4 4 (:TYPE-PRESCRIPTION SET::EMPTYP-TYPE))
 (4 4 (:REWRITE DM::PERM-MEMBER))
 (4 4 (:REWRITE SET::IN-SET))
 (2 2 (:REWRITE MOD-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (2 2 (:REWRITE |(mod x (- y))| . 3))
 (2 2 (:REWRITE |(mod x (- y))| . 2))
 (2 2 (:REWRITE |(mod x (- y))| . 1))
 (2 2 (:REWRITE |(mod x (* y (/ z))) not rewriting-goal-literal|))
 (2 2 (:REWRITE |(mod (* x (/ y)) z) not rewriting-goal-literal|))
 (2 2 (:REWRITE |(expt 1/c n)|))
 (2 2 (:REWRITE |(expt (- x) n)|))
 )