(EVAL-POLYNOMIAL-EXPT-CORRECT-LEMMA
 (465 305 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (305 305 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (305 305 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (305 305 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (305 305 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (305 305 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (291 42 (:REWRITE DEFAULT-PLUS-1))
 (236 35 (:REWRITE DEFAULT-TIMES-2))
 (234 35 (:REWRITE DEFAULT-TIMES-1))
 (148 37 (:REWRITE RATIONALP-X))
 (144 16 (:REWRITE ACL2-NUMBERP-X))
 (97 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (97 7 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (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))
 (66 3 (:REWRITE |(+ (if a b c) x)|))
 (42 42 (:REWRITE REDUCE-INTEGERP-+))
 (42 42 (:REWRITE INTEGERP-MINUS-X))
 (42 42 (:META META-INTEGERP-CORRECT))
 (39 3 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (37 37 (:REWRITE REDUCE-RATIONALP-+))
 (37 37 (:REWRITE REDUCE-RATIONALP-*))
 (37 37 (:REWRITE RATIONALP-MINUS-X))
 (37 37 (:META META-RATIONALP-CORRECT))
 (28 28 (:REWRITE DEFAULT-CAR))
 (23 23 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (13 13 (:TYPE-PRESCRIPTION RATIONALP-EXPT-TYPE-PRESCRIPTION))
 (13 13 (:REWRITE DEFAULT-EXPT-2))
 (13 13 (:REWRITE DEFAULT-EXPT-1))
 (13 13 (:REWRITE |(expt 1/c n)|))
 (13 13 (:REWRITE |(expt (- x) n)|))
 (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 2 (:REWRITE |(+ c (+ d x))|))
 (5 5 (:REWRITE THE-FLOOR-BELOW))
 (5 5 (:REWRITE THE-FLOOR-ABOVE))
 (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-SUMS-<))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5 5 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (5 5 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (5 5 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (5 5 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5 5 (:REWRITE INTEGERP-<-CONSTANT))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-2))
 (5 5 (:REWRITE DEFAULT-LESS-THAN-1))
 (5 5 (:REWRITE CONSTANT-<-INTEGERP))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (5 5 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< c (- x))|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (5 5 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (5 5 (:REWRITE |(< (/ x) 0)|))
 (5 5 (:REWRITE |(< (/ x) (/ y))|))
 (5 5 (:REWRITE |(< (- x) c)|))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE |(* x (if a b c))|))
 (1 1 (:REWRITE |(* c (expt d n))|))
 (1 1 (:REWRITE |(* c (* d x))|))
 )
(EVAL-POLYNOMIAL-EXPT-CORRECT
 (59 1 (:DEFINITION EVAL-POLYNOMIAL-EXPT-AUX))
 (47 1 (:DEFINITION EVAL-POLYNOMIAL))
 (36 4 (:REWRITE ACL2-NUMBERP-X))
 (35 6 (:REWRITE DEFAULT-PLUS-2))
 (28 7 (:REWRITE RATIONALP-X))
 (27 5 (:REWRITE DEFAULT-TIMES-1))
 (11 1 (:REWRITE |(+ (if a b c) x)|))
 (7 7 (:REWRITE REDUCE-RATIONALP-+))
 (7 7 (:REWRITE REDUCE-RATIONALP-*))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE RATIONALP-MINUS-X))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-RATIONALP-CORRECT))
 (7 7 (:META META-INTEGERP-CORRECT))
 (7 5 (:REWRITE DEFAULT-TIMES-2))
 (6 5 (:REWRITE DEFAULT-PLUS-1))
 (6 1 (:REWRITE |(+ y x)|))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (4 1 (:REWRITE |(* y x)|))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 1 (:REWRITE |(+ 0 x)|))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-POSITIVE-BASE))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONNEGATIVE-BASE))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NON-0-BASE))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1 1 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (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)|))
 )
(REAL-POLYNOMIAL-SCALE-POLYNOMIAL
 (60 15 (:REWRITE RATIONALP-X))
 (45 5 (:REWRITE DEFAULT-TIMES-2))
 (36 4 (:REWRITE ACL2-NUMBERP-X))
 (15 15 (:REWRITE REDUCE-RATIONALP-+))
 (15 15 (:REWRITE REDUCE-RATIONALP-*))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE RATIONALP-MINUS-X))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (15 15 (:META META-RATIONALP-CORRECT))
 (15 15 (:META META-INTEGERP-CORRECT))
 (12 11 (:REWRITE DEFAULT-CAR))
 (9 8 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE DEFAULT-TIMES-1))
 )
(EVAL-SCALE-POLYNOMIAL
 (153 20 (:REWRITE DEFAULT-PLUS-2))
 (148 37 (:REWRITE RATIONALP-X))
 (126 14 (:REWRITE ACL2-NUMBERP-X))
 (82 28 (:REWRITE DEFAULT-TIMES-2))
 (37 37 (:REWRITE REDUCE-RATIONALP-+))
 (37 37 (:REWRITE REDUCE-RATIONALP-*))
 (37 37 (:REWRITE REDUCE-INTEGERP-+))
 (37 37 (:REWRITE RATIONALP-MINUS-X))
 (37 37 (:REWRITE INTEGERP-MINUS-X))
 (37 37 (:META META-RATIONALP-CORRECT))
 (37 37 (:META META-INTEGERP-CORRECT))
 (28 25 (:REWRITE DEFAULT-CAR))
 (26 26 (:REWRITE DEFAULT-TIMES-1))
 (22 15 (:REWRITE DEFAULT-PLUS-1))
 (19 19 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (17 14 (:REWRITE DEFAULT-CDR))
 (9 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (9 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (9 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8 8 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (8 8 (:REWRITE NORMALIZE-ADDENDS))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (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))|))
 (2 2 (:REWRITE |(* c (* d x))|))
 )
(EVAL-SCALE-EXPT-POLYNOMIAL
 (94 2 (:DEFINITION EVAL-POLYNOMIAL))
 (58 6 (:REWRITE DEFAULT-PLUS-2))
 (36 9 (:REWRITE RATIONALP-X))
 (36 4 (:REWRITE ACL2-NUMBERP-X))
 (33 3 (:DEFINITION RATIONAL-POLYNOMIAL-P))
 (12 2 (:REWRITE |(+ y x)|))
 (10 10 (:TYPE-PRESCRIPTION EVAL-POLYNOMIAL))
 (9 9 (:REWRITE REDUCE-RATIONALP-+))
 (9 9 (:REWRITE REDUCE-RATIONALP-*))
 (9 9 (:REWRITE REDUCE-INTEGERP-+))
 (9 9 (:REWRITE RATIONALP-MINUS-X))
 (9 9 (:REWRITE INTEGERP-MINUS-X))
 (9 9 (:META META-RATIONALP-CORRECT))
 (9 9 (:META META-INTEGERP-CORRECT))
 (8 4 (:REWRITE DEFAULT-TIMES-2))
 (6 4 (:REWRITE DEFAULT-PLUS-1))
 (5 5 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE DEFAULT-TIMES-1))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 )
(CONSP-SCALE-POLNOMIAL
 (108 12 (:REWRITE ACL2-NUMBERP-X))
 (48 12 (:REWRITE RATIONALP-X))
 (12 12 (:REWRITE REDUCE-RATIONALP-+))
 (12 12 (:REWRITE REDUCE-RATIONALP-*))
 (12 12 (:REWRITE REDUCE-INTEGERP-+))
 (12 12 (:REWRITE RATIONALP-MINUS-X))
 (12 12 (:REWRITE INTEGERP-MINUS-X))
 (12 12 (:META META-RATIONALP-CORRECT))
 (12 12 (:META META-INTEGERP-CORRECT))
 (6 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (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))|))
 )
(REAL-POLYNOMIAL-+
 (116 29 (:REWRITE RATIONALP-X))
 (105 7 (:REWRITE DEFAULT-PLUS-2))
 (90 10 (:REWRITE ACL2-NUMBERP-X))
 (47 5 (:REWRITE DEFAULT-PLUS-1))
 (35 34 (:REWRITE DEFAULT-CAR))
 (29 29 (:REWRITE REDUCE-RATIONALP-+))
 (29 29 (:REWRITE REDUCE-RATIONALP-*))
 (29 29 (:REWRITE REDUCE-INTEGERP-+))
 (29 29 (:REWRITE RATIONALP-MINUS-X))
 (29 29 (:REWRITE INTEGERP-MINUS-X))
 (29 29 (:META META-RATIONALP-CORRECT))
 (29 29 (:META META-INTEGERP-CORRECT))
 (13 12 (:REWRITE DEFAULT-CDR))
 (9 9 (:TYPE-PRESCRIPTION POLYNOMIAL-+))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (3 3 (:REWRITE NORMALIZE-ADDENDS))
 )
(EVAL-POLYNOMIAL-+
 (550 504 (:REWRITE DEFAULT-CAR))
 (426 350 (:REWRITE DEFAULT-PLUS-1))
 (425 110 (:REWRITE RATIONALP-X))
 (405 196 (:REWRITE DEFAULT-TIMES-2))
 (288 32 (:REWRITE ACL2-NUMBERP-X))
 (275 229 (:REWRITE DEFAULT-CDR))
 (196 196 (:REWRITE DEFAULT-TIMES-1))
 (110 110 (:REWRITE REDUCE-RATIONALP-+))
 (110 110 (:REWRITE REDUCE-RATIONALP-*))
 (110 110 (:REWRITE RATIONALP-MINUS-X))
 (110 110 (:META META-RATIONALP-CORRECT))
 (106 106 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (105 105 (:REWRITE REDUCE-INTEGERP-+))
 (105 105 (:REWRITE INTEGERP-MINUS-X))
 (105 105 (:META META-INTEGERP-CORRECT))
 (28 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (22 22 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (12 12 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (12 12 (:REWRITE |(equal c (/ x))|))
 (12 12 (:REWRITE |(equal (/ x) (/ y))|))
 (12 12 (:REWRITE |(equal (- x) (- y))|))
 (11 11 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (11 11 (:REWRITE |(equal c (- x))|))
 (11 11 (:REWRITE |(equal (- x) c)|))
 (11 11 (:REWRITE |(+ c (+ d x))|))
 (7 7 (:REWRITE FOLD-CONSTS-IN-+))
 (7 7 (:REWRITE |(equal (+ (- c) x) y)|))
 (6 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (4 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (3 3 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (1 1 (:REWRITE DEFAULT-DIVIDE))
 (1 1 (:REWRITE |(not (equal x (/ y)))|))
 (1 1 (:REWRITE |(equal x (if a b c))|))
 (1 1 (:REWRITE |(equal x (/ y))|))
 (1 1 (:REWRITE |(equal (if a b c) x)|))
 )
(EVAL-POLYNOMIAL-EXPT-+
 (188 4 (:DEFINITION EVAL-POLYNOMIAL))
 (120 14 (:REWRITE DEFAULT-PLUS-2))
 (72 8 (:REWRITE ACL2-NUMBERP-X))
 (66 6 (:DEFINITION RATIONAL-POLYNOMIAL-P))
 (60 15 (:REWRITE RATIONALP-X))
 (24 4 (:REWRITE |(+ y x)|))
 (20 20 (:TYPE-PRESCRIPTION EVAL-POLYNOMIAL))
 (16 10 (:REWRITE DEFAULT-PLUS-1))
 (15 15 (:REWRITE REDUCE-RATIONALP-+))
 (15 15 (:REWRITE REDUCE-RATIONALP-*))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE RATIONALP-MINUS-X))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (15 15 (:META META-RATIONALP-CORRECT))
 (15 15 (:META META-INTEGERP-CORRECT))
 (10 10 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE DEFAULT-CAR))
 (8 4 (:REWRITE DEFAULT-TIMES-2))
 (6 6 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (6 6 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE DEFAULT-TIMES-1))
 )
(CONSP-POLNOMIAL-+
 (208 12 (:REWRITE DEFAULT-PLUS-2))
 (180 20 (:REWRITE ACL2-NUMBERP-X))
 (92 8 (:REWRITE DEFAULT-PLUS-1))
 (80 20 (:REWRITE RATIONALP-X))
 (20 20 (:REWRITE REDUCE-RATIONALP-+))
 (20 20 (:REWRITE REDUCE-RATIONALP-*))
 (20 20 (:REWRITE REDUCE-INTEGERP-+))
 (20 20 (:REWRITE RATIONALP-MINUS-X))
 (20 20 (:REWRITE INTEGERP-MINUS-X))
 (20 20 (:META META-RATIONALP-CORRECT))
 (20 20 (:META META-INTEGERP-CORRECT))
 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (2 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE |(equal x (if a b c))|))
 (1 1 (:REWRITE |(equal c (/ x))|))
 (1 1 (:REWRITE |(equal c (- x))|))
 (1 1 (:REWRITE |(equal (if a b 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))|))
 )
(REAL-POLYNOMIAL-*
 (180 16 (:REWRITE ACL2-NUMBERP-X))
 (180 3 (:DEFINITION POLYNOMIAL-+))
 (126 27 (:REWRITE RATIONALP-X))
 (123 9 (:REWRITE DEFAULT-PLUS-1))
 (115 3 (:DEFINITION SCALE-POLYNOMIAL))
 (106 8 (:REWRITE DEFAULT-TIMES-2))
 (63 63 (:TYPE-PRESCRIPTION SCALE-POLYNOMIAL))
 (45 5 (:REWRITE DEFAULT-TIMES-1))
 (37 24 (:REWRITE DEFAULT-CAR))
 (34 21 (:REWRITE DEFAULT-CDR))
 (27 27 (:REWRITE REDUCE-RATIONALP-+))
 (27 27 (:REWRITE REDUCE-RATIONALP-*))
 (27 27 (:REWRITE REDUCE-INTEGERP-+))
 (27 27 (:REWRITE RATIONALP-MINUS-X))
 (27 27 (:REWRITE INTEGERP-MINUS-X))
 (27 27 (:META META-RATIONALP-CORRECT))
 (27 27 (:META META-INTEGERP-CORRECT))
 (12 3 (:REWRITE |(+ y x)|))
 (9 9 (:REWRITE DEFAULT-PLUS-2))
 (9 9 (:REWRITE CONSP-SCALE-POLNOMIAL))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE |(+ 0 x)|))
 )
(EVAL-POLYNOMIAL-*
 (396 40 (:REWRITE ACL2-NUMBERP-X))
 (367 51 (:REWRITE DEFAULT-PLUS-2))
 (262 61 (:REWRITE RATIONALP-X))
 (180 3 (:DEFINITION POLYNOMIAL-+))
 (169 39 (:REWRITE DEFAULT-PLUS-1))
 (161 36 (:REWRITE DEFAULT-TIMES-2))
 (115 3 (:DEFINITION SCALE-POLYNOMIAL))
 (82 33 (:REWRITE DEFAULT-TIMES-1))
 (63 63 (:TYPE-PRESCRIPTION SCALE-POLYNOMIAL))
 (61 61 (:REWRITE REDUCE-RATIONALP-+))
 (61 61 (:REWRITE REDUCE-RATIONALP-*))
 (61 61 (:REWRITE REDUCE-INTEGERP-+))
 (61 61 (:REWRITE RATIONALP-MINUS-X))
 (61 61 (:REWRITE INTEGERP-MINUS-X))
 (61 61 (:META META-RATIONALP-CORRECT))
 (61 61 (:META META-INTEGERP-CORRECT))
 (61 46 (:REWRITE DEFAULT-CAR))
 (55 40 (:REWRITE DEFAULT-CDR))
 (26 26 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (15 15 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (15 15 (:REWRITE NORMALIZE-ADDENDS))
 (12 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9 9 (:REWRITE CONSP-SCALE-POLNOMIAL))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (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))|))
 )
(EVAL-POLYNOMIAL-EXPT-*
 (188 4 (:DEFINITION EVAL-POLYNOMIAL))
 (116 12 (:REWRITE DEFAULT-PLUS-2))
 (72 8 (:REWRITE ACL2-NUMBERP-X))
 (66 6 (:DEFINITION RATIONAL-POLYNOMIAL-P))
 (60 15 (:REWRITE RATIONALP-X))
 (24 4 (:REWRITE |(+ y x)|))
 (20 20 (:TYPE-PRESCRIPTION EVAL-POLYNOMIAL))
 (15 15 (:REWRITE REDUCE-RATIONALP-+))
 (15 15 (:REWRITE REDUCE-RATIONALP-*))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE RATIONALP-MINUS-X))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (15 15 (:META META-RATIONALP-CORRECT))
 (15 15 (:META META-INTEGERP-CORRECT))
 (12 8 (:REWRITE DEFAULT-PLUS-1))
 (12 6 (:REWRITE DEFAULT-TIMES-2))
 (10 10 (:REWRITE DEFAULT-CDR))
 (10 10 (:REWRITE DEFAULT-CAR))
 (8 6 (:REWRITE DEFAULT-TIMES-1))
 (6 6 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 )
(CONSP-POLNOMIAL-*
 (198 18 (:REWRITE ACL2-NUMBERP-X))
 (180 3 (:DEFINITION POLYNOMIAL-+))
 (135 3 (:DEFINITION SCALE-POLYNOMIAL))
 (126 9 (:REWRITE DEFAULT-TIMES-2))
 (123 9 (:REWRITE DEFAULT-PLUS-1))
 (90 18 (:REWRITE RATIONALP-X))
 (66 6 (:REWRITE DEFAULT-TIMES-1))
 (24 12 (:REWRITE DEFAULT-CDR))
 (24 12 (:REWRITE DEFAULT-CAR))
 (18 18 (:REWRITE REDUCE-RATIONALP-+))
 (18 18 (:REWRITE REDUCE-RATIONALP-*))
 (18 18 (:REWRITE REDUCE-INTEGERP-+))
 (18 18 (:REWRITE RATIONALP-MINUS-X))
 (18 18 (:REWRITE INTEGERP-MINUS-X))
 (18 18 (:META META-RATIONALP-CORRECT))
 (18 18 (:META META-INTEGERP-CORRECT))
 (12 3 (:REWRITE |(+ y x)|))
 (9 9 (:REWRITE DEFAULT-PLUS-2))
 (6 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE CDR-CONS))
 (3 3 (:REWRITE CAR-CONS))
 (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 |(+ 0 x)|))
 )
(NUMBERP-CAR-POLY
 (28 7 (:REWRITE RATIONALP-X))
 (18 2 (:REWRITE ACL2-NUMBERP-X))
 (7 7 (:REWRITE REDUCE-RATIONALP-+))
 (7 7 (:REWRITE REDUCE-RATIONALP-*))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE RATIONALP-MINUS-X))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-RATIONALP-CORRECT))
 (7 7 (:META META-INTEGERP-CORRECT))
 (6 6 (:REWRITE DEFAULT-CAR))
 (4 4 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-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))|))
 )
