(M1::PSI-CLOCK)
(M1::TMI3-SIMULATION
 (2150 10 (:DEFINITION M1::TMI3))
 (1890 30 (:DEFINITION M1::NINSTR))
 (300 150 (:TYPE-PRESCRIPTION M1::NATP-NST-IN))
 (285 102 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (273 102 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (252 102 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (190 190 (:TYPE-PRESCRIPTION M1::CURRENT-SYMN))
 (150 150 (:TYPE-PRESCRIPTION M1::NSYM))
 (150 150 (:TYPE-PRESCRIPTION M1::NATP-NCAR))
 (102 102 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (102 102 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (102 102 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (102 102 (:REWRITE |(equal c (/ x))|))
 (102 102 (:REWRITE |(equal c (- x))|))
 (102 102 (:REWRITE |(equal (/ x) c)|))
 (102 102 (:REWRITE |(equal (/ x) (/ y))|))
 (102 102 (:REWRITE |(equal (- x) c)|))
 (102 102 (:REWRITE |(equal (- x) (- y))|))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (83 83 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (80 40 (:TYPE-PRESCRIPTION M1::INTEGERP-NINSTR))
 (40 40 (:REWRITE ZP-OPEN))
 (31 1 (:REWRITE ODD-EXPT-THM))
 (31 1 (:LINEAR EXPT-<=-1-TWO))
 (30 1 (:LINEAR EXPT->-1-ONE))
 (29 11 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (26 1 (:LINEAR EXPT-X->=-X))
 (26 1 (:LINEAR EXPT-X->-X))
 (20 11 (:REWRITE SIMPLIFY-SUMS-<))
 (20 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (20 11 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (20 11 (:REWRITE DEFAULT-LESS-THAN-2))
 (14 2 (:REWRITE ACL2-NUMBERP-X))
 (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-ADDITIVE-CONSTANT-<))
 (11 11 (:REWRITE INTEGERP-<-CONSTANT))
 (11 11 (:REWRITE DEFAULT-LESS-THAN-1))
 (11 11 (:REWRITE CONSTANT-<-INTEGERP))
 (11 11 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (11 11 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (11 11 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (11 11 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (11 11 (:REWRITE |(< c (- x))|))
 (11 11 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (11 11 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (11 11 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (11 11 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (11 11 (:REWRITE |(< (/ x) (/ y))|))
 (11 11 (:REWRITE |(< (- x) c)|))
 (11 11 (:REWRITE |(< (- x) (- y))|))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE DEFAULT-PLUS-2))
 (10 10 (:REWRITE DEFAULT-PLUS-1))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:META META-INTEGERP-CORRECT))
 (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 |(< (/ x) 0)|))
 (5 5 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE DEFAULT-EXPT-2))
 (4 4 (:REWRITE DEFAULT-EXPT-1))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 (4 1 (:REWRITE RATIONALP-X))
 (4 1 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (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 |(< 0 (/ x))|))
 (3 3 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (2 2 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (2 2 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (2 2 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (1 1 (:REWRITE REDUCE-RATIONALP-+))
 (1 1 (:REWRITE REDUCE-RATIONALP-*))
 (1 1 (:REWRITE RATIONALP-MINUS-X))
 (1 1 (:META META-RATIONALP-CORRECT))
 (1 1 (:LINEAR M1::PROPERTIES-OF-INSTR))
 (1 1 (:LINEAR M1::LOG2-IMPLIES-EXPT-UPPERBOUND-COROLLARY . 1))
 (1 1 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (1 1 (:LINEAR EXPT-LINEAR-UPPER-<))
 (1 1 (:LINEAR EXPT-LINEAR-LOWER-<))
 (1 1 (:LINEAR EXPT->=-1-TWO))
 (1 1 (:LINEAR EXPT->-1-TWO))
 (1 1 (:LINEAR EXPT-<=-1-ONE))
 (1 1 (:LINEAR EXPT-<-1-TWO))
 (1 1 (:LINEAR EXPT-<-1-ONE))
 )
(M1::INTEGERP-MV-NTH-CONVERT-TAPE-TO-TAPEN-POS
 (286 2 (:DEFINITION M1::HALF-TAPE))
 (280 2 (:DEFINITION M1::SYMP))
 (274 6 (:DEFINITION MEMBER-EQUAL))
 (243 24 (:REWRITE DEFAULT-PLUS-2))
 (216 24 (:REWRITE ACL2-NUMBERP-X))
 (213 24 (:REWRITE DEFAULT-PLUS-1))
 (204 4 (:DEFINITION M1::CONVERT-HALF-TAPE-TO-NAT))
 (114 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (64 16 (:REWRITE RATIONALP-X))
 (64 16 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (42 8 (:REWRITE DEFAULT-TIMES-2))
 (35 5 (:DEFINITION LEN))
 (33 33 (:REWRITE INTEGERP-MINUS-X))
 (32 32 (:META META-INTEGERP-CORRECT))
 (30 30 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (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 8 (:REWRITE DEFAULT-TIMES-1))
 (29 29 (:REWRITE DEFAULT-CAR))
 (25 25 (:REWRITE DEFAULT-CDR))
 (18 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (16 16 (:REWRITE REDUCE-RATIONALP-+))
 (16 16 (:REWRITE REDUCE-RATIONALP-*))
 (16 16 (:REWRITE RATIONALP-MINUS-X))
 (16 16 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (16 16 (:META META-RATIONALP-CORRECT))
 (16 2 (:DEFINITION M1::REV))
 (10 10 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (10 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE M1::MEMBER-SUBSETP))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (10 4 (:REWRITE DEFAULT-EXPT-2))
 (10 2 (:DEFINITION BINARY-APPEND))
 (6 6 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (5 1 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (4 4 (:REWRITE DEFAULT-EXPT-1))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 (4 4 (:REWRITE |(+ c (+ d x))|))
 (3 3 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE INTEGERP-+-REDUCE-CONSTANT))
 )
(M1::NONNEG-MV-NTH-CONVERT-TAPE-TO-TAPEN-POS
 (286 2 (:DEFINITION M1::HALF-TAPE))
 (280 2 (:DEFINITION M1::SYMP))
 (274 6 (:DEFINITION MEMBER-EQUAL))
 (256 5 (:DEFINITION M1::CONVERT-HALF-TAPE-TO-NAT))
 (242 26 (:REWRITE ACL2-NUMBERP-X))
 (228 21 (:REWRITE DEFAULT-PLUS-1))
 (124 21 (:REWRITE DEFAULT-PLUS-2))
 (114 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (72 18 (:REWRITE RATIONALP-X))
 (72 18 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (46 9 (:REWRITE DEFAULT-TIMES-2))
 (44 44 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (44 44 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (44 44 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (44 44 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (44 44 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (36 36 (:REWRITE REDUCE-INTEGERP-+))
 (36 36 (:REWRITE INTEGERP-MINUS-X))
 (36 36 (:META META-INTEGERP-CORRECT))
 (35 5 (:DEFINITION LEN))
 (31 9 (:REWRITE DEFAULT-TIMES-1))
 (30 30 (:REWRITE DEFAULT-CAR))
 (29 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (29 2 (:REWRITE DEFAULT-LESS-THAN-1))
 (28 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (26 26 (:REWRITE DEFAULT-CDR))
 (18 18 (:REWRITE REDUCE-RATIONALP-+))
 (18 18 (:REWRITE REDUCE-RATIONALP-*))
 (18 18 (:REWRITE RATIONALP-MINUS-X))
 (18 18 (:META META-RATIONALP-CORRECT))
 (18 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (16 16 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (16 16 (:REWRITE NORMALIZE-ADDENDS))
 (16 2 (:DEFINITION M1::REV))
 (10 10 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (10 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE M1::MEMBER-SUBSETP))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (10 4 (:REWRITE DEFAULT-EXPT-2))
 (10 2 (:DEFINITION BINARY-APPEND))
 (7 7 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (4 4 (:REWRITE DEFAULT-EXPT-1))
 (4 4 (:REWRITE |(expt 1/c n)|))
 (4 4 (:REWRITE |(expt (- x) n)|))
 (2 2 (:REWRITE THE-FLOOR-BELOW))
 (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 REDUCE-ADDITIVE-CONSTANT-<))
 (2 2 (:REWRITE INTEGERP-<-CONSTANT))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 (2 2 (:REWRITE DEFAULT-LESS-THAN-2))
 (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) 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 (+ d x))|))
 (1 1 (:REWRITE |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 )
(M1::POSITIVE-NATP-NCODE-REWRITE-VERSION
 (4 4 (:TYPE-PRESCRIPTION NATP))
 )
(M1::TAPEP-NEW-TAPE
 (1196 104 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1176 168 (:REWRITE ACL2-NUMBERP-X))
 (336 84 (:REWRITE RATIONALP-X))
 (336 84 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (188 104 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (168 168 (:REWRITE REDUCE-INTEGERP-+))
 (168 168 (:REWRITE INTEGERP-MINUS-X))
 (168 168 (:REWRITE DEFAULT-CAR))
 (168 168 (:META META-INTEGERP-CORRECT))
 (114 114 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (114 114 (:REWRITE M1::MEMBER-SUBSETP))
 (105 105 (:REWRITE DEFAULT-CDR))
 (104 104 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (104 104 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (104 104 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (104 104 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (104 104 (:REWRITE |(equal c (/ x))|))
 (104 104 (:REWRITE |(equal c (- x))|))
 (104 104 (:REWRITE |(equal (/ x) c)|))
 (104 104 (:REWRITE |(equal (/ x) (/ y))|))
 (104 104 (:REWRITE |(equal (- x) c)|))
 (104 104 (:REWRITE |(equal (- x) (- y))|))
 (84 84 (:REWRITE REDUCE-RATIONALP-+))
 (84 84 (:REWRITE REDUCE-RATIONALP-*))
 (84 84 (:REWRITE RATIONALP-MINUS-X))
 (84 84 (:META META-RATIONALP-CORRECT))
 (40 40 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (10 10 (:REWRITE |(equal x (if a b c))|))
 (10 10 (:REWRITE |(equal (if a b c) x)|))
 )
(M1::OPERATIONP-NTH-2-INSTR
 (7676 1244 (:REWRITE ACL2-NUMBERP-X))
 (7607 622 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (5270 34 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (5168 34 (:DEFINITION M1::HALF-TAPE))
 (2703 17 (:DEFINITION TRUE-LISTP))
 (2144 536 (:REWRITE RATIONALP-X))
 (2144 536 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (1175 622 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1072 1072 (:REWRITE REDUCE-INTEGERP-+))
 (1072 1072 (:REWRITE INTEGERP-MINUS-X))
 (1072 1072 (:META META-INTEGERP-CORRECT))
 (1071 1071 (:REWRITE DEFAULT-CAR))
 (794 622 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (622 622 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (622 622 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (622 622 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (622 622 (:REWRITE |(equal c (/ x))|))
 (622 622 (:REWRITE |(equal c (- x))|))
 (622 622 (:REWRITE |(equal (/ x) c)|))
 (622 622 (:REWRITE |(equal (/ x) (/ y))|))
 (622 622 (:REWRITE |(equal (- x) c)|))
 (622 622 (:REWRITE |(equal (- x) (- y))|))
 (536 536 (:REWRITE REDUCE-RATIONALP-+))
 (536 536 (:REWRITE REDUCE-RATIONALP-*))
 (536 536 (:REWRITE RATIONALP-MINUS-X))
 (536 536 (:META META-RATIONALP-CORRECT))
 (417 417 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (417 417 (:REWRITE M1::MEMBER-SUBSETP))
 (179 179 (:REWRITE DEFAULT-CDR))
 (170 170 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (142 142 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (119 17 (:DEFINITION LEN))
 (34 17 (:REWRITE DEFAULT-PLUS-2))
 (17 17 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (17 17 (:REWRITE NORMALIZE-ADDENDS))
 (17 17 (:REWRITE DEFAULT-PLUS-1))
 )
(M1::SYMBOLP-NTH-3-INSTR
 (3392 288 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (3370 514 (:REWRITE ACL2-NUMBERP-X))
 (3100 20 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (3040 20 (:DEFINITION M1::HALF-TAPE))
 (1590 10 (:DEFINITION TRUE-LISTP))
 (952 238 (:REWRITE RATIONALP-X))
 (952 238 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (536 288 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (476 476 (:REWRITE REDUCE-INTEGERP-+))
 (476 476 (:REWRITE INTEGERP-MINUS-X))
 (476 476 (:META META-INTEGERP-CORRECT))
 (464 464 (:REWRITE DEFAULT-CAR))
 (326 288 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (288 288 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (288 288 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (288 288 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (288 288 (:REWRITE |(equal c (/ x))|))
 (288 288 (:REWRITE |(equal c (- x))|))
 (288 288 (:REWRITE |(equal (/ x) c)|))
 (288 288 (:REWRITE |(equal (/ x) (/ y))|))
 (288 288 (:REWRITE |(equal (- x) c)|))
 (288 288 (:REWRITE |(equal (- x) (- y))|))
 (240 240 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (240 240 (:REWRITE M1::MEMBER-SUBSETP))
 (238 238 (:REWRITE REDUCE-RATIONALP-+))
 (238 238 (:REWRITE REDUCE-RATIONALP-*))
 (238 238 (:REWRITE RATIONALP-MINUS-X))
 (238 238 (:META META-RATIONALP-CORRECT))
 (100 100 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (90 90 (:REWRITE DEFAULT-CDR))
 (80 80 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (80 80 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (70 10 (:DEFINITION LEN))
 (20 10 (:REWRITE DEFAULT-PLUS-2))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE DEFAULT-PLUS-1))
 )
(M1::TAPEP-TMI
 (4392 6 (:DEFINITION M1::TURING-MACHINEP))
 (4368 6 (:DEFINITION M1::TURING-4-TUPLE))
 (4020 84 (:DEFINITION MEMBER-EQUAL))
 (2568 18 (:DEFINITION M1::SYMP))
 (2100 198 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2040 312 (:REWRITE ACL2-NUMBERP-X))
 (1860 12 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (1824 12 (:DEFINITION M1::HALF-TAPE))
 (1524 6 (:DEFINITION M1::OPERATIONP))
 (954 6 (:DEFINITION TRUE-LISTP))
 (576 144 (:REWRITE RATIONALP-X))
 (576 144 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (372 198 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (288 288 (:REWRITE REDUCE-INTEGERP-+))
 (288 288 (:REWRITE INTEGERP-MINUS-X))
 (288 288 (:META META-INTEGERP-CORRECT))
 (258 258 (:REWRITE DEFAULT-CAR))
 (246 198 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (198 198 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (198 198 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (198 198 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (198 198 (:REWRITE |(equal c (/ x))|))
 (198 198 (:REWRITE |(equal c (- x))|))
 (198 198 (:REWRITE |(equal (/ x) c)|))
 (198 198 (:REWRITE |(equal (/ x) (/ y))|))
 (198 198 (:REWRITE |(equal (- x) c)|))
 (198 198 (:REWRITE |(equal (- x) (- y))|))
 (144 144 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (144 144 (:REWRITE REDUCE-RATIONALP-+))
 (144 144 (:REWRITE REDUCE-RATIONALP-*))
 (144 144 (:REWRITE RATIONALP-MINUS-X))
 (144 144 (:REWRITE M1::MEMBER-SUBSETP))
 (144 144 (:META META-RATIONALP-CORRECT))
 (102 102 (:REWRITE DEFAULT-CDR))
 (60 60 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (48 48 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (48 48 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (42 6 (:DEFINITION LEN))
 (36 36 (:TYPE-PRESCRIPTION LEN))
 (16 10 (:REWRITE DEFAULT-PLUS-2))
 (12 12 (:DEFINITION M1::STATE-NAMEP))
 (10 10 (:REWRITE ZP-OPEN))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE DEFAULT-PLUS-1))
 )
(M1::FIND-K
 (12 6 (:TYPE-PRESCRIPTION M1::NATP-CDR-ASSOC-MAP))
 (6 6 (:TYPE-PRESCRIPTION M1::NATP-MAP))
 )
(M1::SIMULATION
 (81472 8 (:DEFINITION M1::TMI3))
 (81080 24 (:REWRITE M1::NINSTR-NCODE))
 (47994 63 (:DEFINITION M1::TM-TO-TM1))
 (39493 3100 (:REWRITE DEFAULT-CDR))
 (37603 431 (:REWRITE M1::CONSP-ASSOC))
 (37060 526 (:DEFINITION M1::NAT-TO-NAT-ALISTP))
 (35236 484 (:REWRITE M1::NAT-TO-NAT-ALISTP-TO-ALISTP))
 (34412 52 (:DEFINITION M1::MAX-WIDTH1))
 (23452 104 (:DEFINITION M1::LOG2))
 (19758 2622 (:REWRITE ACL2-NUMBERP-X))
 (19070 242 (:DEFINITION ALISTP))
 (18434 2122 (:REWRITE DEFAULT-LESS-THAN-2))
 (17568 96 (:DEFINITION M1::DESCENDING-MAP))
 (15114 2026 (:REWRITE DEFAULT-LESS-THAN-1))
 (13133 439 (:DEFINITION ASSOC-EQUAL))
 (10969 921 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (9348 104 (:DEFINITION MAX))
 (7800 84 (:DEFINITION M1::INSTR))
 (7608 48 (:REWRITE M1::MAPPED-INSTR))
 (7608 48 (:REWRITE M1::INSTR-IMPLIES-MAPPED-INSTR-VICE-VERSA))
 (6384 1416 (:REWRITE RATIONALP-X))
 (5134 3938 (:REWRITE INTEGERP-MINUS-X))
 (5088 1272 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (4568 4568 (:REWRITE DEFAULT-CAR))
 (3900 52 (:REWRITE |(< x (if a b c))|))
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 (714 714 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (662 662 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (662 662 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (662 662 (:REWRITE |(< (/ x) 0)|))
 (662 662 (:REWRITE |(< (* x y) 0)|))
 (646 646 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (645 645 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (645 645 (:REWRITE |(equal c (/ x))|))
 (645 645 (:REWRITE |(equal c (- x))|))
 (645 645 (:REWRITE |(equal (/ x) c)|))
 (645 645 (:REWRITE |(equal (/ x) (/ y))|))
 (645 645 (:REWRITE |(equal (- x) c)|))
 (645 645 (:REWRITE |(equal (- x) (- y))|))
 (641 20 (:REWRITE ODD-EXPT-THM))
 (511 214 (:REWRITE ZP-OPEN))
 (375 375 (:REWRITE |(< (+ c/d x) y)|))
 (375 375 (:REWRITE |(< (+ (- c) x) y)|))
 (248 8 (:LINEAR EXPT-<=-1-TWO))
 (240 8 (:LINEAR EXPT->-1-ONE))
 (208 8 (:LINEAR EXPT-X->=-X))
 (208 8 (:LINEAR EXPT-X->-X))
 (75 75 (:REWRITE REDUCE-INTEGERP-+))
 (75 75 (:REWRITE INTEGERP-MINUS-X))
 (75 75 (:META META-INTEGERP-CORRECT))
 (63 63 (:TYPE-PRESCRIPTION M1::!NOP))
 (54 50 (:REWRITE DEFAULT-CAR))
 (45 45 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (45 45 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (45 45 (:REWRITE DEFAULT-EXPT-2))
 (45 45 (:REWRITE DEFAULT-EXPT-1))
 (45 45 (:REWRITE |(expt 1/c n)|))
 (45 45 (:REWRITE |(expt (- x) n)|))
 (45 45 (:REWRITE |(< 0 (/ x))|))
 (45 45 (:REWRITE |(< 0 (* x y))|))
 (44 22 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (30 30 (:TYPE-PRESCRIPTION M1::!NINSTR1))
 (26 26 (:REWRITE |(equal (+ (- c) x) y)|))
 (16 16 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (16 16 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (16 16 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (12 12 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (9 9 (:REWRITE |(< y (+ (- c) x))|))
 (9 9 (:REWRITE |(< x (+ c/d y))|))
 (8 8 (:LINEAR M1::LOG2-IMPLIES-EXPT-UPPERBOUND-COROLLARY . 1))
 (8 8 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (8 8 (:LINEAR EXPT-LINEAR-UPPER-<))
 (8 8 (:LINEAR EXPT-LINEAR-LOWER-<))
 (8 8 (:LINEAR EXPT->=-1-TWO))
 (8 8 (:LINEAR EXPT->-1-TWO))
 (8 8 (:LINEAR EXPT-<=-1-ONE))
 (8 8 (:LINEAR EXPT-<-1-TWO))
 (8 8 (:LINEAR EXPT-<-1-ONE))
 (7 6 (:REWRITE DEFAULT-CDR))
 )
(M1::POSITIVE-K-HALT
 (76 33 (:REWRITE DEFAULT-PLUS-2))
 (36 33 (:REWRITE DEFAULT-PLUS-1))
 (36 1 (:REWRITE M1::!CURRENT-SYMN-SPEC))
 (34 1 (:DEFINITION NATP))
 (19 9 (:REWRITE DEFAULT-LESS-THAN-1))
 (12 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (12 6 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE NORMALIZE-ADDENDS))
 (10 6 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (9 9 (:REWRITE THE-FLOOR-BELOW))
 (9 9 (:REWRITE THE-FLOOR-ABOVE))
 (9 9 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (9 9 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (9 9 (:REWRITE DEFAULT-LESS-THAN-2))
 (6 6 (:REWRITE SIMPLIFY-SUMS-<))
 (6 6 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (6 6 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (6 6 (:REWRITE INTEGERP-<-CONSTANT))
 (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) (/ y))|))
 (6 6 (:REWRITE |(< (- x) c)|))
 (6 6 (:REWRITE |(< (- x) (- y))|))
 (6 6 (:REWRITE |(< (* x y) 0)|))
 (4 4 (:REWRITE FOLD-CONSTS-IN-+))
 (4 4 (:REWRITE |(< (+ c/d 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 |(< (/ x) 0)|))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(M1::POSITIVE-K-STEP
 (1090 190 (:REWRITE DEFAULT-PLUS-2))
 (217 190 (:REWRITE DEFAULT-PLUS-1))
 (217 46 (:REWRITE DEFAULT-LESS-THAN-1))
 (119 29 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (119 29 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (110 29 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (106 3 (:DEFINITION NATP))
 (65 65 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (65 65 (:REWRITE NORMALIZE-ADDENDS))
 (58 58 (:REWRITE FOLD-CONSTS-IN-+))
 (46 46 (:REWRITE THE-FLOOR-BELOW))
 (46 46 (:REWRITE THE-FLOOR-ABOVE))
 (46 46 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (46 46 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (46 46 (:REWRITE DEFAULT-LESS-THAN-2))
 (42 1 (:REWRITE M1::!NOP-SPEC))
 (41 6 (:REWRITE M1::!CURRENT-SYMN-SPEC))
 (38 3 (:REWRITE M1::!NINSTR1-SPEC))
 (32 32 (:REWRITE |(< (+ c/d x) y)|))
 (29 29 (:REWRITE SIMPLIFY-SUMS-<))
 (29 29 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (29 29 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (29 29 (:REWRITE INTEGERP-<-CONSTANT))
 (29 29 (:REWRITE CONSTANT-<-INTEGERP))
 (29 29 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (29 29 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (29 29 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (29 29 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (29 29 (:REWRITE |(< c (- x))|))
 (29 29 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (29 29 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (29 29 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (29 29 (:REWRITE |(< (/ x) (/ y))|))
 (29 29 (:REWRITE |(< (- x) c)|))
 (29 29 (:REWRITE |(< (- x) (- y))|))
 (29 29 (:REWRITE |(< (* x y) 0)|))
 (15 15 (:REWRITE |(< (+ (- c) x) y)|))
 (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)|))
 (6 6 (:TYPE-PRESCRIPTION M1::!NINSTR1))
 (3 3 (:TYPE-PRESCRIPTION NATP))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:META META-INTEGERP-CORRECT))
 )
(M1::POSITIVE-K*
 (37 37 (:REWRITE DEFAULT-CAR))
 (15 8 (:REWRITE DEFAULT-PLUS-2))
 (15 8 (:REWRITE DEFAULT-PLUS-1))
 (6 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (3 3 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (3 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (3 3 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (3 3 (:REWRITE DEFAULT-CDR))
 (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))|))
 )
(M1::TRACE-EXTENSION
 (5687 828 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (3853 717 (:REWRITE ACL2-NUMBERP-X))
 (2816 72 (:LINEAR M1::INTEGERP-NINSTR))
 (2586 828 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2228 828 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1056 244 (:REWRITE RATIONALP-X))
 (1040 240 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (828 828 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (828 828 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (828 828 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (828 828 (:REWRITE |(equal c (/ x))|))
 (828 828 (:REWRITE |(equal c (- x))|))
 (828 828 (:REWRITE |(equal (/ x) c)|))
 (828 828 (:REWRITE |(equal (/ x) (/ y))|))
 (828 828 (:REWRITE |(equal (- x) c)|))
 (828 828 (:REWRITE |(equal (- x) (- y))|))
 (806 806 (:REWRITE REDUCE-INTEGERP-+))
 (806 806 (:REWRITE INTEGERP-MINUS-X))
 (806 806 (:META META-INTEGERP-CORRECT))
 (326 326 (:REWRITE THE-FLOOR-BELOW))
 (326 326 (:REWRITE THE-FLOOR-ABOVE))
 (326 326 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (326 326 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (326 326 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (326 326 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (326 326 (:REWRITE INTEGERP-<-CONSTANT))
 (326 326 (:REWRITE DEFAULT-LESS-THAN-2))
 (326 326 (:REWRITE DEFAULT-LESS-THAN-1))
 (326 326 (:REWRITE CONSTANT-<-INTEGERP))
 (326 326 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (326 326 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (326 326 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (326 326 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (326 326 (:REWRITE |(< c (- x))|))
 (326 326 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (326 326 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (326 326 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (326 326 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (326 326 (:REWRITE |(< (/ x) (/ y))|))
 (326 326 (:REWRITE |(< (- x) c)|))
 (326 326 (:REWRITE |(< (- x) (- y))|))
 (325 325 (:REWRITE |(< (/ x) 0)|))
 (325 325 (:REWRITE |(< (* x y) 0)|))
 (323 323 (:REWRITE SIMPLIFY-SUMS-<))
 (323 323 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (323 323 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (322 322 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (322 322 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (240 240 (:REWRITE REDUCE-RATIONALP-+))
 (240 240 (:REWRITE REDUCE-RATIONALP-*))
 (240 240 (:REWRITE RATIONALP-MINUS-X))
 (240 240 (:META META-RATIONALP-CORRECT))
 (234 234 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (234 234 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (234 234 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (234 234 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (234 234 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (234 234 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (153 115 (:REWRITE DEFAULT-CDR))
 (153 115 (:REWRITE DEFAULT-CAR))
 (35 35 (:REWRITE DEFAULT-PLUS-2))
 (35 35 (:REWRITE DEFAULT-PLUS-1))
 (32 32 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (32 32 (:REWRITE NORMALIZE-ADDENDS))
 (9 9 (: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 |(< y (+ (- c) x))|))
 (1 1 (:REWRITE |(< x (+ c/d y))|))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(M1::TRACEP)
(M1::TRACEP-TMI3-TRACE
 (229 37 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (165 33 (:REWRITE ACL2-NUMBERP-X))
 (108 3 (:LINEAR M1::INTEGERP-NINSTR))
 (97 37 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (81 37 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (44 11 (:REWRITE RATIONALP-X))
 (44 11 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (37 37 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (37 37 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (37 37 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (37 37 (:REWRITE |(equal c (/ x))|))
 (37 37 (:REWRITE |(equal c (- x))|))
 (37 37 (:REWRITE |(equal (/ x) c)|))
 (37 37 (:REWRITE |(equal (/ x) (/ y))|))
 (37 37 (:REWRITE |(equal (- x) c)|))
 (37 37 (:REWRITE |(equal (- x) (- y))|))
 (36 36 (:REWRITE REDUCE-INTEGERP-+))
 (36 36 (:REWRITE INTEGERP-MINUS-X))
 (36 36 (:META META-INTEGERP-CORRECT))
 (16 16 (:REWRITE ZP-OPEN))
 (14 14 (:REWRITE THE-FLOOR-BELOW))
 (14 14 (:REWRITE THE-FLOOR-ABOVE))
 (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 SIMPLIFY-SUMS-<))
 (14 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (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 REDUCE-ADDITIVE-CONSTANT-<))
 (14 14 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (14 14 (:REWRITE INTEGERP-<-CONSTANT))
 (14 14 (:REWRITE DEFAULT-LESS-THAN-2))
 (14 14 (:REWRITE DEFAULT-LESS-THAN-1))
 (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) 0)|))
 (14 14 (:REWRITE |(< (/ x) (/ y))|))
 (14 14 (:REWRITE |(< (- x) c)|))
 (14 14 (:REWRITE |(< (- x) (- y))|))
 (14 14 (:REWRITE |(< (* x y) 0)|))
 (11 11 (:REWRITE REDUCE-RATIONALP-+))
 (11 11 (:REWRITE REDUCE-RATIONALP-*))
 (11 11 (:REWRITE RATIONALP-MINUS-X))
 (11 11 (:META META-RATIONALP-CORRECT))
 (11 10 (:REWRITE DEFAULT-CAR))
 (9 8 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-PLUS-2))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 )
(M1::K*-APPEND
 (414 207 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (231 210 (:REWRITE DEFAULT-CAR))
 (207 207 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (207 207 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (158 77 (:REWRITE DEFAULT-PLUS-2))
 (155 77 (:REWRITE DEFAULT-PLUS-1))
 (145 28 (:LINEAR M1::POSITIVE-K*))
 (55 43 (:REWRITE DEFAULT-CDR))
 (34 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (34 11 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (29 29 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (11 11 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (11 11 (:REWRITE |(equal c (/ x))|))
 (11 11 (:REWRITE |(equal c (- x))|))
 (11 11 (:REWRITE |(equal (/ x) c)|))
 (11 11 (:REWRITE |(equal (/ x) (/ y))|))
 (11 11 (:REWRITE |(equal (- x) c)|))
 (11 11 (:REWRITE |(equal (- x) (- y))|))
 (8 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (5 5 (:REWRITE |(equal (+ (- c) x) y)|))
 (1 1 (:REWRITE FOLD-CONSTS-IN-+))
 (1 1 (:REWRITE |(+ c (+ d x))|))
 )
(M1::TRACEP-APPEND
 (1262 631 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (631 631 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (20 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (20 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (20 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (6 6 (:REWRITE |(equal x (if a b c))|))
 (6 6 (:REWRITE |(equal (if a b c) x)|))
 )
(M1::TMI3-V-LAST-TMI3-TRACE
 (580 86 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (444 84 (:REWRITE ACL2-NUMBERP-X))
 (220 86 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (216 6 (:LINEAR M1::INTEGERP-NINSTR))
 (182 86 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (120 30 (:REWRITE RATIONALP-X))
 (120 30 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (92 92 (:REWRITE REDUCE-INTEGERP-+))
 (92 92 (:REWRITE INTEGERP-MINUS-X))
 (92 92 (:META META-INTEGERP-CORRECT))
 (86 86 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (86 86 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (86 86 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (86 86 (:REWRITE |(equal c (/ x))|))
 (86 86 (:REWRITE |(equal c (- x))|))
 (86 86 (:REWRITE |(equal (/ x) c)|))
 (86 86 (:REWRITE |(equal (/ x) (/ y))|))
 (86 86 (:REWRITE |(equal (- x) c)|))
 (86 86 (:REWRITE |(equal (- x) (- y))|))
 (54 10 (:REWRITE DEFAULT-CAR))
 (35 35 (:REWRITE THE-FLOOR-BELOW))
 (35 35 (:REWRITE THE-FLOOR-ABOVE))
 (35 35 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (35 35 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (35 35 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (35 35 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (35 35 (:REWRITE INTEGERP-<-CONSTANT))
 (35 35 (:REWRITE DEFAULT-LESS-THAN-2))
 (35 35 (:REWRITE DEFAULT-LESS-THAN-1))
 (35 35 (:REWRITE CONSTANT-<-INTEGERP))
 (35 35 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (35 35 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (35 35 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (35 35 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (35 35 (:REWRITE |(< c (- x))|))
 (35 35 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (35 35 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (35 35 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (35 35 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (35 35 (:REWRITE |(< (/ x) 0)|))
 (35 35 (:REWRITE |(< (/ x) (/ y))|))
 (35 35 (:REWRITE |(< (- x) c)|))
 (35 35 (:REWRITE |(< (- x) (- y))|))
 (35 35 (:REWRITE |(< (* x y) 0)|))
 (32 32 (:REWRITE ZP-OPEN))
 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (32 32 (:REWRITE SIMPLIFY-SUMS-<))
 (32 32 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (32 32 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (30 30 (:REWRITE REDUCE-RATIONALP-+))
 (30 30 (:REWRITE REDUCE-RATIONALP-*))
 (30 30 (:REWRITE RATIONALP-MINUS-X))
 (30 30 (:META META-RATIONALP-CORRECT))
 (30 11 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (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))
 )
(M1::K*-TMI3-TRACE-MONOTONIC
 (4346 41 (:DEFINITION M1::NINSTR))
 (3836 11 (:DEFINITION M1::TMI3))
 (828 139 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (704 2 (:DEFINITION M1::TMI3-TRACE))
 (629 125 (:REWRITE ACL2-NUMBERP-X))
 (360 139 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (303 139 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (205 205 (:TYPE-PRESCRIPTION M1::POSITIVE-NATP-NNIL))
 (205 205 (:TYPE-PRESCRIPTION M1::NSYM))
 (168 42 (:REWRITE RATIONALP-X))
 (168 42 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (164 82 (:TYPE-PRESCRIPTION M1::NATP-NST-IN))
 (139 139 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (139 139 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (139 139 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (139 139 (:REWRITE |(equal c (/ x))|))
 (139 139 (:REWRITE |(equal c (- x))|))
 (139 139 (:REWRITE |(equal (/ x) c)|))
 (139 139 (:REWRITE |(equal (/ x) (/ y))|))
 (139 139 (:REWRITE |(equal (- x) c)|))
 (139 139 (:REWRITE |(equal (- x) (- y))|))
 (126 126 (:REWRITE REDUCE-INTEGERP-+))
 (126 126 (:REWRITE INTEGERP-MINUS-X))
 (126 126 (:META META-INTEGERP-CORRECT))
 (82 82 (:TYPE-PRESCRIPTION M1::NATP-NCAR))
 (78 41 (:REWRITE DEFAULT-PLUS-2))
 (68 41 (:REWRITE DEFAULT-PLUS-1))
 (61 47 (:REWRITE DEFAULT-LESS-THAN-2))
 (54 54 (:REWRITE ZP-OPEN))
 (54 46 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (54 46 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (50 47 (:REWRITE DEFAULT-LESS-THAN-1))
 (47 47 (:REWRITE THE-FLOOR-BELOW))
 (47 47 (:REWRITE THE-FLOOR-ABOVE))
 (46 46 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (46 46 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (46 46 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (46 46 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (46 46 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (46 46 (:REWRITE INTEGERP-<-CONSTANT))
 (46 46 (:REWRITE CONSTANT-<-INTEGERP))
 (46 46 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (46 46 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (46 46 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (46 46 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (46 46 (:REWRITE |(< c (- x))|))
 (46 46 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (46 46 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (46 46 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (46 46 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (46 46 (:REWRITE |(< (/ x) (/ y))|))
 (46 46 (:REWRITE |(< (- x) c)|))
 (46 46 (:REWRITE |(< (- x) (- y))|))
 (42 42 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (42 42 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (42 42 (:REWRITE REDUCE-RATIONALP-+))
 (42 42 (:REWRITE REDUCE-RATIONALP-*))
 (42 42 (:REWRITE RATIONALP-MINUS-X))
 (42 42 (:REWRITE |(< (/ x) 0)|))
 (42 42 (:REWRITE |(< (* x y) 0)|))
 (42 42 (:META META-RATIONALP-CORRECT))
 (35 29 (:REWRITE DEFAULT-CAR))
 (25 25 (:TYPE-PRESCRIPTION M1::TMI3-TRACE))
 (21 21 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (15 9 (:REWRITE DEFAULT-CDR))
 (11 1 (:DEFINITION LAST))
 (10 2 (:DEFINITION BINARY-APPEND))
 (8 4 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (8 2 (:LINEAR M1::POSITIVE-K*))
 (6 3 (:TYPE-PRESCRIPTION LAST))
 (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 |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 )
(M1::FINAL-TMI3-STATE-IS-PROPER
 (2216 2216 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-ODD-EXPONENT))
 (2216 2216 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (2216 2216 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (2216 2216 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (2216 2216 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (2216 2216 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (945 33 (:REWRITE ODD-EXPT-THM))
 (620 20 (:LINEAR EXPT-<=-1-TWO))
 (600 20 (:LINEAR EXPT->-1-ONE))
 (558 234 (:REWRITE DEFAULT-LESS-THAN-2))
 (546 231 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (529 229 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (520 20 (:LINEAR EXPT-X->=-X))
 (520 20 (:LINEAR EXPT-X->-X))
 (512 190 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (512 190 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (502 229 (:REWRITE SIMPLIFY-SUMS-<))
 (502 229 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (480 190 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (234 234 (:REWRITE THE-FLOOR-BELOW))
 (234 234 (:REWRITE THE-FLOOR-ABOVE))
 (231 231 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (231 231 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (231 231 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (231 231 (:REWRITE INTEGERP-<-CONSTANT))
 (231 231 (:REWRITE CONSTANT-<-INTEGERP))
 (231 231 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (231 231 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (231 231 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (231 231 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (231 231 (:REWRITE |(< c (- x))|))
 (231 231 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (231 231 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
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 (231 231 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (231 231 (:REWRITE |(< (/ x) (/ y))|))
 (231 231 (:REWRITE |(< (- x) c)|))
 (231 231 (:REWRITE |(< (- x) (- y))|))
 (190 190 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (190 190 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (190 190 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (190 190 (:REWRITE |(equal c (/ x))|))
 (190 190 (:REWRITE |(equal c (- x))|))
 (190 190 (:REWRITE |(equal (/ x) c)|))
 (190 190 (:REWRITE |(equal (/ x) (/ y))|))
 (190 190 (:REWRITE |(equal (- x) c)|))
 (190 190 (:REWRITE |(equal (- x) (- y))|))
 (103 103 (:REWRITE REDUCE-INTEGERP-+))
 (103 103 (:REWRITE INTEGERP-MINUS-X))
 (103 103 (:META META-INTEGERP-CORRECT))
 (93 93 (:REWRITE DEFAULT-EXPT-2))
 (93 93 (:REWRITE DEFAULT-EXPT-1))
 (93 93 (:REWRITE |(expt 1/c n)|))
 (93 93 (:REWRITE |(expt (- x) n)|))
 (88 88 (:REWRITE |(< (/ x) 0)|))
 (88 88 (:REWRITE |(< (* x y) 0)|))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (86 86 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (78 78 (:REWRITE ZP-OPEN))
 (78 6 (:REWRITE ACL2-NUMBERP-X))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (73 73 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (73 73 (:REWRITE |(< 0 (/ x))|))
 (73 73 (:REWRITE |(< 0 (* x y))|))
 (40 40 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (40 40 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (40 40 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (24 6 (:REWRITE RATIONALP-X))
 (24 6 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (20 20 (:LINEAR M1::LOG2-IMPLIES-EXPT-UPPERBOUND-COROLLARY . 1))
 (20 20 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (20 20 (:LINEAR EXPT-LINEAR-UPPER-<))
 (20 20 (:LINEAR EXPT-LINEAR-LOWER-<))
 (20 20 (:LINEAR EXPT->=-1-TWO))
 (20 20 (:LINEAR EXPT->-1-TWO))
 (20 20 (:LINEAR EXPT-<=-1-ONE))
 (20 20 (:LINEAR EXPT-<-1-TWO))
 (20 20 (:LINEAR EXPT-<-1-ONE))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE NORMALIZE-ADDENDS))
 (11 11 (:REWRITE DEFAULT-PLUS-2))
 (11 11 (:REWRITE DEFAULT-PLUS-1))
 (6 6 (:REWRITE REDUCE-RATIONALP-+))
 (6 6 (:REWRITE REDUCE-RATIONALP-*))
 (6 6 (:REWRITE RATIONALP-MINUS-X))
 (6 6 (:META META-RATIONALP-CORRECT))
 )
(M1::ACL2-NUMBERP-CDR-ASSOC-EQUAL-ST-RENAMING-MAP-ST
 (3050 1 (:DEFINITION M1::RENAMING-MAP1))
 (2530 5 (:REWRITE M1::INSTR-IMPLIES-ASSOC))
 (2518 4 (:DEFINITION M1::TURING-MACHINEP))
 (2498 4 (:DEFINITION M1::TURING-4-TUPLE))
 (1482 6 (:DEFINITION M1::SYMP))
 (1035 175 (:REWRITE ACL2-NUMBERP-X))
 (1032 4 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (1020 4 (:DEFINITION M1::HALF-TAPE))
 (1018 93 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (906 2 (:DEFINITION M1::OPERATIONP))
 (530 2 (:DEFINITION TRUE-LISTP))
 (422 6 (:REWRITE M1::NAT-TO-NAT-ALISTP-TO-ALISTP))
 (406 6 (:DEFINITION M1::NAT-TO-NAT-ALISTP))
 (340 10 (:DEFINITION NATP))
 (292 73 (:REWRITE RATIONALP-X))
 (284 71 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (188 188 (:REWRITE DEFAULT-CAR))
 (166 93 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (154 154 (:REWRITE REDUCE-INTEGERP-+))
 (154 154 (:REWRITE INTEGERP-MINUS-X))
 (154 154 (:META META-INTEGERP-CORRECT))
 (124 93 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (93 93 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (93 93 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (93 93 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (93 93 (:REWRITE |(equal c (/ x))|))
 (93 93 (:REWRITE |(equal c (- x))|))
 (93 93 (:REWRITE |(equal (/ x) c)|))
 (93 93 (:REWRITE |(equal (/ x) (/ y))|))
 (93 93 (:REWRITE |(equal (- x) c)|))
 (93 93 (:REWRITE |(equal (- x) (- y))|))
 (71 71 (:REWRITE REDUCE-RATIONALP-+))
 (71 71 (:REWRITE REDUCE-RATIONALP-*))
 (71 71 (:REWRITE RATIONALP-MINUS-X))
 (71 71 (:META META-RATIONALP-CORRECT))
 (60 60 (:REWRITE DEFAULT-CDR))
 (53 53 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (53 53 (:REWRITE M1::MEMBER-SUBSETP))
 (43 16 (:TYPE-PRESCRIPTION M1::NATP-CDR-ASSOC-MAP))
 (40 40 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (22 22 (:TYPE-PRESCRIPTION M1::NAT-TO-NAT-ALISTP))
 (20 20 (:TYPE-PRESCRIPTION LEN))
 (20 20 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (16 16 (:TYPE-PRESCRIPTION M1::NATP-MAP))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (14 2 (:DEFINITION LEN))
 (13 13 (:TYPE-PRESCRIPTION M1::TURING-MACHINEP))
 (11 11 (:TYPE-PRESCRIPTION M1::RENAMING-MAP2))
 (11 4 (:REWRITE DEFAULT-PLUS-2))
 (10 10 (:REWRITE THE-FLOOR-BELOW))
 (10 10 (:REWRITE THE-FLOOR-ABOVE))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (10 10 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (10 10 (:REWRITE SIMPLIFY-SUMS-<))
 (10 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (10 10 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (10 10 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (10 10 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (10 10 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (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) 0)|))
 (10 10 (:REWRITE |(< (/ x) (/ y))|))
 (10 10 (:REWRITE |(< (- x) c)|))
 (10 10 (:REWRITE |(< (- x) (- y))|))
 (10 10 (:REWRITE |(< (* x y) 0)|))
 (10 1 (:REWRITE |(+ y x)|))
 (9 4 (:REWRITE DEFAULT-PLUS-1))
 (8 8 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (4 4 (:DEFINITION M1::STATE-NAMEP))
 (3 3 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (3 3 (:REWRITE NORMALIZE-ADDENDS))
 )
(M1::FIND-K-MONOTONIC
 (1112268 1442 (:DEFINITION M1::TM-TO-TM1))
 (830626 746 (:DEFINITION MEMBER-EQUAL))
 (829786 146 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (829672 38 (:DEFINITION M1::HALF-TAPE))
 (824859 52667 (:REWRITE DEFAULT-CDR))
 (795925 9075 (:REWRITE M1::CONSP-ASSOC))
 (748858 9498 (:REWRITE M1::NAT-TO-NAT-ALISTP-TO-ALISTP))
 (741402 9771 (:DEFINITION M1::NAT-TO-NAT-ALISTP))
 (706332 79 (:DEFINITION M1::TURING-MACHINEP))
 (705656 79 (:DEFINITION M1::TURING-4-TUPLE))
 (701472 120 (:REWRITE M1::CAR-INSTR))
 (674252 117 (:DEFINITION M1::SYMP))
 (466466 79 (:DEFINITION M1::OPERATIONP))
 (424898 10 (:REWRITE M1::NST-OUT-MAKE-CELL))
 (415185 55 (:DEFINITION TRUE-LISTP))
 (402923 4749 (:DEFINITION ALISTP))
 (285160 9140 (:DEFINITION ASSOC-EQUAL))
 (279108 17 (:LINEAR M1::NST-OUT-BOUND))
 (264179 41713 (:REWRITE ACL2-NUMBERP-X))
 (251004 365 (:DEFINITION M1::MAX-WIDTH1))
 (196313 15344 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (173960 730 (:DEFINITION M1::LOG2))
 (163064 28486 (:REWRITE DEFAULT-LESS-THAN-2))
 (145835 8 (:REWRITE M1::NOP-MAKE-CELL))
 (145119 793 (:DEFINITION M1::DESCENDING-MAP))
 (82261 82249 (:REWRITE DEFAULT-CAR))
 (74592 18404 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (68514 59314 (:REWRITE INTEGERP-MINUS-X))
 (65745 730 (:DEFINITION MAX))
 (65083 445 (:REWRITE M1::MAPPED-INSTR))
 (64322 440 (:REWRITE M1::INSTR-IMPLIES-MAPPED-INSTR-VICE-VERSA))
 (58914 58914 (:REWRITE REDUCE-INTEGERP-+))
 (58914 58914 (:META META-INTEGERP-CORRECT))
 (48945 48945 (:TYPE-PRESCRIPTION M1::NAT-TO-NAT-ALISTP))
 (46849 843 (:REWRITE ZP-OPEN))
 (31580 15344 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (30223 25642 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (30223 25642 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (29472 3 (:DEFINITION M1::TMI3-TRACE))
 (28486 28486 (:REWRITE THE-FLOOR-BELOW))
 (28486 28486 (:REWRITE THE-FLOOR-ABOVE))
 (27200 400 (:REWRITE FLOOR-ZERO . 3))
 (27192 15344 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (26286 36 (:DEFINITION M1::NINSTR))
 (26060 25660 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (26060 25660 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (25660 25660 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (25660 25660 (:REWRITE INTEGERP-<-CONSTANT))
 (25660 25660 (:REWRITE CONSTANT-<-INTEGERP))
 (25660 25660 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (25660 25660 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (25660 25660 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (25660 25660 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (25660 25660 (:REWRITE |(< c (- x))|))
 (25660 25660 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (25660 25660 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (25660 25660 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (25660 25660 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (25660 25660 (:REWRITE |(< (/ x) (/ y))|))
 (25660 25660 (:REWRITE |(< (- x) c)|))
 (25660 25660 (:REWRITE |(< (- x) (- y))|))
 (21532 175 (:REWRITE M1::INSTR-IMPLIES-MAPPED-INSTR))
 (21200 400 (:REWRITE CANCEL-FLOOR-+))
 (20805 20805 (:TYPE-PRESCRIPTION M1::LOG2))
 (20185 20185 (:REWRITE |(< (/ x) 0)|))
 (20185 20185 (:REWRITE |(< (* x y) 0)|))
 (20167 20167 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (20167 20167 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (18404 18404 (:REWRITE REDUCE-RATIONALP-+))
 (18404 18404 (:REWRITE REDUCE-RATIONALP-*))
 (18404 18404 (:REWRITE RATIONALP-MINUS-X))
 (18404 18404 (:META META-RATIONALP-CORRECT))
 (15839 20 (:REWRITE M1::TURING1-4-TUPLE-INSTR))
 (15344 15344 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (15344 15344 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (15344 15344 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (15344 15344 (:REWRITE |(equal c (/ x))|))
 (15344 15344 (:REWRITE |(equal c (- x))|))
 (15344 15344 (:REWRITE |(equal (/ x) c)|))
 (15344 15344 (:REWRITE |(equal (/ x) (/ y))|))
 (15344 15344 (:REWRITE |(equal (- x) c)|))
 (15344 15344 (:REWRITE |(equal (- x) (- y))|))
 (13185 365 (:REWRITE M1::LOG2-IMPLIES-EXPT-UPPERBOUND))
 (12000 400 (:REWRITE FLOOR-ZERO . 4))
 (12000 400 (:REWRITE FLOOR-X-Y-=-1 . 2))
 (11259 139 (:LINEAR M1::NAT-TO-NAT-ALISTP-PROPERTY))
 (10731 237 (:REWRITE M1::NAT-TO-NAT-ALISTP-PROPERTY . 1))
 (9320 2330 (:REWRITE |(* y x)|))
 (8990 8990 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (8990 8990 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (8990 8990 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (8990 8990 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (8800 400 (:REWRITE FLOOR-=-X/Y . 3))
 (8800 400 (:REWRITE FLOOR-=-X/Y . 2))
 (8650 730 (:REWRITE |(floor x 2)| . 1))
 (8030 730 (:REWRITE DEFAULT-FLOOR-RATIO))
 (7930 730 (:REWRITE |(floor x 2)| . 2))
 (7250 7250 (:REWRITE DEFAULT-TIMES-2))
 (7250 7250 (:REWRITE DEFAULT-TIMES-1))
 (7144 188 (:LINEAR EXPT-<=-1-TWO))
 (6956 188 (:LINEAR EXPT->-1-ONE))
 (6876 2508 (:REWRITE DEFAULT-PLUS-2))
 (6800 800 (:REWRITE |(* (- x) y)|))
 (6204 188 (:LINEAR EXPT-X->=-X))
 (6204 188 (:LINEAR EXPT-X->-X))
 (6000 6000 (:TYPE-PRESCRIPTION NOT-INTEGERP-4B))
 (6000 6000 (:TYPE-PRESCRIPTION NOT-INTEGERP-3B))
 (6000 6000 (:TYPE-PRESCRIPTION NOT-INTEGERP-2B))
 (6000 6000 (:TYPE-PRESCRIPTION NOT-INTEGERP-1B))
 (4520 4520 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (4000 800 (:REWRITE DEFAULT-MINUS))
 (3982 1991 (:TYPE-PRESCRIPTION M1::NATP-CDR-ASSOC-MAP))
 (3965 3965 (:TYPE-PRESCRIPTION M1::DESCENDING-MAP))
 (3600 800 (:REWRITE |(- (* c x))|))
 (2670 2508 (:REWRITE DEFAULT-PLUS-1))
 (2013 2013 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2000 400 (:REWRITE FLOOR-ZERO . 5))
 (2000 400 (:REWRITE FLOOR-ZERO . 2))
 (2000 400 (:REWRITE FLOOR-X-Y-=-1 . 3))
 (2000 400 (:REWRITE FLOOR-X-Y-=--1 . 3))
 (2000 400 (:REWRITE FLOOR-X-Y-=--1 . 2))
 (2000 400 (:REWRITE FLOOR-CANCEL-*-NOT-REWRITING-GOAL-LITERAL))
 (2000 400 (:REWRITE FLOOR-CANCEL-*-CONST))
 (2000 400 (:REWRITE |(floor (* x (/ y)) z) not rewriting-goal-literal|))
 (1955 1955 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (1955 1955 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (1955 1955 (:REWRITE |(< 0 (/ x))|))
 (1955 1955 (:REWRITE |(< 0 (* x y))|))
 (1461 1461 (:REWRITE M1::ACL2-NUMBERP-CDR-ASSOC-EQUAL-ST-RENAMING-MAP-ST))
 (1296 1296 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (1296 1296 (:REWRITE M1::MEMBER-SUBSETP))
 (1105 1105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NONPOSITIVE-BASE-EVEN-EXPONENT))
 (1105 1105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-ODD-EXPONENT))
 (1105 1105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-NEGATIVE-BASE-EVEN-EXPONENT))
 (1105 1105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-B))
 (1105 1105 (:TYPE-PRESCRIPTION EXPT-TYPE-PRESCRIPTION-INTEGERP-BASE-A))
 (1016 1016 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (934 467 (:REWRITE DEFAULT-EXPT-2))
 (912 24 (:REWRITE ODD-EXPT-THM))
 (800 800 (:TYPE-PRESCRIPTION ABS))
 (787 787 (:TYPE-PRESCRIPTION M1::NEW-TAPE1))
 (750 180 (:TYPE-PRESCRIPTION M1::NATP-NST-IN))
 (738 738 (:REWRITE |(< y (+ (- c) x))|))
 (738 738 (:REWRITE |(< x (+ c/d y))|))
 (730 730 (:REWRITE DEFAULT-FLOOR-2))
 (730 730 (:REWRITE DEFAULT-FLOOR-1))
 (637 91 (:DEFINITION LEN))
 (596 188 (:LINEAR EXPT-LINEAR-LOWER-<=))
 (514 514 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (467 467 (:REWRITE DEFAULT-EXPT-1))
 (467 467 (:REWRITE |(expt 1/c n)|))
 (467 467 (:REWRITE |(expt (- x) n)|))
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 (412 46 (:TYPE-PRESCRIPTION M1::INTEGERP-NINSTR))
 (400 400 (:REWRITE FLOOR-CANCEL-*-REWRITING-GOAL-LITERAL))
 (400 400 (:REWRITE |(floor x (- y))| . 2))
 (400 400 (:REWRITE |(floor x (- y))| . 1))
 (400 400 (:REWRITE |(floor x (* y (/ z))) rewriting-goal-literal|))
 (400 400 (:REWRITE |(floor x (* y (/ z))) not rewriting-goal-literal|))
 (400 400 (:REWRITE |(floor (- x) y)| . 2))
 (400 400 (:REWRITE |(floor (- x) y)| . 1))
 (400 400 (:REWRITE |(floor (* x (/ y)) z) rewriting-goal-literal|))
 (400 400 (:REWRITE |(< (* (/ x) y) 1) with (< x 0)|))
 (400 400 (:REWRITE |(< (* (/ x) y) 1) with (< 0 x)|))
 (397 397 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (376 376 (:LINEAR EXPT-IS-WEAKLY-INCREASING-FOR-BASE->-1))
 (376 376 (:LINEAR EXPT-IS-WEAKLY-DECREASING-FOR-POS-BASE-<-1))
 (376 376 (:LINEAR EXPT-IS-INCREASING-FOR-BASE->-1))
 (376 376 (:LINEAR EXPT-IS-DECREASING-FOR-POS-BASE-<-1))
 (376 188 (:LINEAR EXPT-<-1-TWO))
 (360 180 (:TYPE-PRESCRIPTION M1::POSITIVE-NATP-NNIL))
 (330 180 (:TYPE-PRESCRIPTION M1::NATP-NCAR))
 (329 329 (:TYPE-PRESCRIPTION M1::TMI))
 (320 64 (:DEFINITION M1::NCODE))
 (253 253 (:TYPE-PRESCRIPTION M1::NST-OUT))
 (188 188 (:LINEAR M1::LOG2-IMPLIES-EXPT-UPPERBOUND-COROLLARY . 1))
 (188 188 (:LINEAR EXPT-LINEAR-UPPER-<=))
 (188 188 (:LINEAR EXPT-LINEAR-UPPER-<))
 (188 188 (:LINEAR EXPT-LINEAR-LOWER-<))
 (188 188 (:LINEAR EXPT->=-1-TWO))
 (188 188 (:LINEAR EXPT->-1-TWO))
 (188 188 (:LINEAR EXPT-<=-1-ONE))
 (188 188 (:LINEAR EXPT-<-1-ONE))
 (158 158 (:DEFINITION M1::STATE-NAMEP))
 (144 144 (:TYPE-PRESCRIPTION M1::NSYM))
 (142 71 (:REWRITE M1::TAPEP-NEW-TAPE1))
 (128 68 (:REWRITE M1::NAT-TO-NAT-ALISTP-PROPERTY . 2))
 (98 12 (:TYPE-PRESCRIPTION M1::NOP-NINSTR))
 (56 56 (:REWRITE |(equal x (if a b c))|))
 (56 56 (:REWRITE |(equal (if a b c) x)|))
 (46 46 (:TYPE-PRESCRIPTION M1::NINSTR))
 (36 36 (:TYPE-PRESCRIPTION M1::TMI3-TRACE))
 (30 30 (:TYPE-PRESCRIPTION M1::NST-IN))
 (30 30 (:TYPE-PRESCRIPTION M1::NCAR))
 (27 27 (:REWRITE |(< (+ c/d x) y)|))
 (27 27 (:REWRITE |(< (+ (- c) x) y)|))
 (26 26 (:REWRITE FOLD-CONSTS-IN-+))
 (22 2 (:DEFINITION LAST))
 (20 4 (:DEFINITION BINARY-APPEND))
 (16 8 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (12 6 (:TYPE-PRESCRIPTION LAST))
 (2 2 (:LINEAR M1::K-NON-0))
 )
(M1::0<-FIND-K
 (1548 2 (:DEFINITION M1::TM-TO-TM1))
 (1237 69 (:REWRITE DEFAULT-CDR))
 (1203 13 (:REWRITE M1::CONSP-ASSOC))
 (1134 14 (:REWRITE M1::NAT-TO-NAT-ALISTP-TO-ALISTP))
 (1092 14 (:DEFINITION M1::NAT-TO-NAT-ALISTP))
 (1054 31 (:DEFINITION NATP))
 (609 7 (:DEFINITION ALISTP))
 (416 13 (:DEFINITION ASSOC-EQUAL))
 (396 1 (:DEFINITION M1::MAX-WIDTH1))
 (251 47 (:REWRITE ACL2-NUMBERP-X))
 (240 19 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (184 2 (:DEFINITION M1::LOG2))
 (181 2 (:DEFINITION MAX))
 (113 113 (:REWRITE DEFAULT-CAR))
 (75 1 (:REWRITE |(< x (if a b c))|))
 (72 2 (:LINEAR M1::K-NON-0))
 (70 70 (:TYPE-PRESCRIPTION M1::NAT-TO-NAT-ALISTP))
 (70 2 (:REWRITE ZP-OPEN))
 (69 69 (:REWRITE REDUCE-INTEGERP-+))
 (69 69 (:REWRITE INTEGERP-MINUS-X))
 (69 69 (:META META-INTEGERP-CORRECT))
 (68 17 (:REWRITE RATIONALP-X))
 (68 17 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (57 57 (:TYPE-PRESCRIPTION M1::LOG2))
 (50 2 (:REWRITE |(floor x 2)| . 1))
 (47 38 (:REWRITE DEFAULT-LESS-THAN-2))
 (43 38 (:REWRITE DEFAULT-LESS-THAN-1))
 (43 37 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (43 37 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (42 37 (:REWRITE SIMPLIFY-SUMS-<))
 (38 38 (:REWRITE THE-FLOOR-BELOW))
 (38 38 (:REWRITE THE-FLOOR-ABOVE))
 (37 37 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (37 37 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (37 37 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (37 37 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (37 37 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (37 37 (:REWRITE INTEGERP-<-CONSTANT))
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 (37 37 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (37 37 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (37 37 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (37 37 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (37 37 (:REWRITE |(< c (- x))|))
 (37 37 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
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 (37 37 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (37 37 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (37 37 (:REWRITE |(< (/ x) (/ y))|))
 (37 37 (:REWRITE |(< (- x) c)|))
 (37 37 (:REWRITE |(< (- x) (- y))|))
 (37 1 (:REWRITE M1::LOG2-IMPLIES-EXPT-UPPERBOUND))
 (36 19 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (35 35 (:TYPE-PRESCRIPTION ALISTP))
 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (32 32 (:REWRITE |(< (/ x) 0)|))
 (32 32 (:REWRITE |(< (* x y) 0)|))
 (32 19 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (22 2 (:REWRITE DEFAULT-FLOOR-RATIO))
 (19 19 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (19 19 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (19 19 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (19 19 (:REWRITE |(equal c (/ x))|))
 (19 19 (:REWRITE |(equal c (- x))|))
 (19 19 (:REWRITE |(equal (/ x) c)|))
 (19 19 (:REWRITE |(equal (/ x) (/ y))|))
 (19 19 (:REWRITE |(equal (- x) c)|))
 (19 19 (:REWRITE |(equal (- x) (- y))|))
 (19 8 (:REWRITE DEFAULT-PLUS-2))
 (17 17 (:REWRITE REDUCE-RATIONALP-+))
 (17 17 (:REWRITE REDUCE-RATIONALP-*))
 (17 17 (:REWRITE RATIONALP-MINUS-X))
 (17 17 (:META META-RATIONALP-CORRECT))
 (16 1 (:REWRITE |(+ x (if a b c))|))
 (15 15 (:TYPE-PRESCRIPTION M1::MAX-WIDTH1))
 (10 10 (:REWRITE DEFAULT-TIMES-2))
 (10 10 (:REWRITE DEFAULT-TIMES-1))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (8 8 (:REWRITE DEFAULT-PLUS-1))
 (8 2 (:REWRITE |(* y x)|))
 (7 7 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (7 7 (:REWRITE NORMALIZE-ADDENDS))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (5 1 (:DEFINITION M1::NCODE))
 (4 4 (:TYPE-PRESCRIPTION M1::TM-TO-TM1))
 (3 3 (:TYPE-PRESCRIPTION NATP))
 (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 DEFAULT-FLOOR-2))
 (2 2 (:REWRITE DEFAULT-FLOOR-1))
 (2 2 (:REWRITE |(floor x 2)| . 2))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 )
(M1::FIND-J1
 (732 1 (:DEFINITION M1::TURING-MACHINEP))
 (728 1 (:DEFINITION M1::TURING-4-TUPLE))
 (670 14 (:DEFINITION MEMBER-EQUAL))
 (428 3 (:DEFINITION M1::SYMP))
 (334 31 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (325 49 (:REWRITE ACL2-NUMBERP-X))
 (310 2 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (304 2 (:DEFINITION M1::HALF-TAPE))
 (254 1 (:DEFINITION M1::OPERATIONP))
 (233 130 (:REWRITE DEFAULT-PLUS-2))
 (204 130 (:REWRITE DEFAULT-PLUS-1))
 (159 1 (:DEFINITION TRUE-LISTP))
 (156 1 (:DEFINITION M1::TMI))
 (150 3 (:DEFINITION M1::INSTR))
 (92 23 (:REWRITE RATIONALP-X))
 (92 23 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (77 38 (:REWRITE DEFAULT-LESS-THAN-1))
 (59 38 (:REWRITE DEFAULT-LESS-THAN-2))
 (59 30 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (58 31 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (49 49 (:REWRITE REDUCE-INTEGERP-+))
 (49 49 (:REWRITE INTEGERP-MINUS-X))
 (49 49 (:META META-INTEGERP-CORRECT))
 (48 48 (:TYPE-PRESCRIPTION M1::TMI))
 (40 40 (:REWRITE DEFAULT-CAR))
 (40 30 (:REWRITE |(< (- x) (- y))|))
 (39 30 (:REWRITE |(< (- x) c)|))
 (38 38 (:REWRITE THE-FLOOR-BELOW))
 (38 38 (:REWRITE THE-FLOOR-ABOVE))
 (37 31 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (32 30 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (31 31 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (31 31 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (31 31 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (31 31 (:REWRITE |(equal c (/ x))|))
 (31 31 (:REWRITE |(equal c (- x))|))
 (31 31 (:REWRITE |(equal (/ x) c)|))
 (31 31 (:REWRITE |(equal (/ x) (/ y))|))
 (31 31 (:REWRITE |(equal (- x) c)|))
 (31 31 (:REWRITE |(equal (- x) (- y))|))
 (31 30 (:REWRITE |(< c (- x))|))
 (30 30 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (30 30 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (30 30 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (30 30 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (30 30 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (30 30 (:REWRITE INTEGERP-<-CONSTANT))
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 (24 24 (:REWRITE M1::MEMBER-SUBSETP))
 (23 23 (:REWRITE REDUCE-RATIONALP-+))
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 (23 23 (:REWRITE RATIONALP-MINUS-X))
 (23 23 (:META META-RATIONALP-CORRECT))
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 (14 14 (:REWRITE |(< (/ x) 0)|))
 (14 14 (:REWRITE |(< (* x y) 0)|))
 (10 10 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (10 10 (:REWRITE |(+ c (+ d x))|))
 (8 8 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (7 7 (:REWRITE FOLD-CONSTS-IN-+))
 (7 1 (:DEFINITION LEN))
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 (6 6 (:REWRITE |(< y (+ (- c) x))|))
 (6 6 (:REWRITE |(< x (+ c/d y))|))
 (6 3 (:REWRITE DEFAULT-MINUS))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (5 5 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (2 2 (:LINEAR M1::K-NON-0))
 (2 2 (:DEFINITION M1::STATE-NAMEP))
 (1 1 (:REWRITE ZP-OPEN))
 (1 1 (:REWRITE |(< 0 (/ x))|))
 (1 1 (:REWRITE |(< 0 (* x y))|))
 )
(M1::FIND-J)
(M1::CRUCIAL-PROPERTY-OF-FIND-J1
 (6586 619 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6400 976 (:REWRITE ACL2-NUMBERP-X))
 (5890 38 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (5776 38 (:DEFINITION M1::HALF-TAPE))
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 (3021 19 (:DEFINITION TRUE-LISTP))
 (1808 452 (:REWRITE RATIONALP-X))
 (1808 452 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (1162 619 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (918 918 (:REWRITE REDUCE-INTEGERP-+))
 (918 918 (:REWRITE INTEGERP-MINUS-X))
 (918 918 (:META META-INTEGERP-CORRECT))
 (805 805 (:REWRITE DEFAULT-CAR))
 (763 619 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (619 619 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (619 619 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (619 619 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (619 619 (:REWRITE |(equal c (/ x))|))
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 (456 456 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (456 456 (:REWRITE M1::MEMBER-SUBSETP))
 (452 452 (:REWRITE REDUCE-RATIONALP-+))
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 (397 397 (:TYPE-PRESCRIPTION M1::TMI))
 (360 360 (:TYPE-PRESCRIPTION M1::NATP-CURRENT-SYM))
 (315 315 (:REWRITE DEFAULT-CDR))
 (190 190 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (152 152 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (152 152 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (133 19 (:DEFINITION LEN))
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 (59 40 (:REWRITE DEFAULT-LESS-THAN-1))
 (58 36 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (58 36 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
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 (49 49 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
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 (47 40 (:REWRITE REMOVE-STRICT-INEQUALITIES))
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 (40 40 (:REWRITE THE-FLOOR-BELOW))
 (40 40 (:REWRITE THE-FLOOR-ABOVE))
 (40 40 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (40 40 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (40 40 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (40 40 (:REWRITE INTEGERP-<-CONSTANT))
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 (40 40 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
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 (40 40 (:REWRITE |(< (/ x) (/ y))|))
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 (40 40 (:REWRITE |(< (- x) (- y))|))
 (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)|))
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 (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 |(< 0 (/ x))|))
 (6 6 (:REWRITE |(< 0 (* x y))|))
 )
(M1::PROGRAM-STEP
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 (188 47 (:REWRITE RATIONALP-X))
 (188 47 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (140 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (94 94 (:REWRITE REDUCE-INTEGERP-+))
 (94 94 (:REWRITE INTEGERP-MINUS-X))
 (94 94 (:META META-INTEGERP-CORRECT))
 (47 47 (:REWRITE REDUCE-RATIONALP-+))
 (47 47 (:REWRITE REDUCE-RATIONALP-*))
 (47 47 (:REWRITE RATIONALP-MINUS-X))
 (47 47 (:META META-RATIONALP-CORRECT))
 (20 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE NORMALIZE-ADDENDS))
 (11 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 10 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (10 10 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (10 10 (:REWRITE |(equal c (/ x))|))
 (10 10 (:REWRITE |(equal c (- x))|))
 (10 10 (:REWRITE |(equal (/ x) c)|))
 (10 10 (:REWRITE |(equal (/ x) (/ y))|))
 (10 10 (:REWRITE |(equal (- x) c)|))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE M1::STEP-OPENER))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (1 1 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 )
(M1::PROGRAM-M1
 (45 9 (:REWRITE ACL2-NUMBERP-X))
 (42 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 3 (:REWRITE RATIONALP-X))
 (12 3 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-INTEGERP-CORRECT))
 (6 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4 4 (:REWRITE ZP-OPEN))
 (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))|))
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 (3 3 (:REWRITE |(equal (- x) (- y))|))
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 (2 2 (:REWRITE M1::STEP-OPENER))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-PLUS-2))
 (2 2 (:REWRITE DEFAULT-PLUS-1))
 )
(M1::M1-STAYS-HALTED
 (43 7 (:REWRITE ACL2-NUMBERP-X))
 (42 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 3 (:REWRITE RATIONALP-X))
 (12 3 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (7 7 (:TYPE-PRESCRIPTION M1::STEP))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-INTEGERP-CORRECT))
 (6 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (4 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))|))
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 (3 3 (:REWRITE |(equal (- x) (- y))|))
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 (2 2 (:REWRITE ZP-OPEN))
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(M1::M1-STAYS-HALTED-CLK+-VERSION
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 (42 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 3 (:REWRITE RATIONALP-X))
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 (6 6 (:REWRITE REDUCE-INTEGERP-+))
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 (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))|))
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 (3 3 (:REWRITE |(equal (- x) c)|))
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 )
(M1::M1-STAYS-HALTED-REPEAT-VERSION
 (28 2 (:REWRITE M1::M1-STAYS-HALTED))
 (14 2 (:REWRITE ACL2-NUMBERP-X))
 (14 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 10 (:REWRITE DEFAULT-PLUS-1))
 (10 10 (:REWRITE DEFAULT-PLUS-2))
 (4 1 (:REWRITE RATIONALP-X))
 (4 1 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (3 3 (:REWRITE THE-FLOOR-BELOW))
 (3 3 (:REWRITE THE-FLOOR-ABOVE))
 (3 3 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (3 3 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (3 3 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (3 3 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (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) (/ y))|))
 (3 3 (:REWRITE |(< (- x) c)|))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:TYPE-PRESCRIPTION BUBBLE-DOWN))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE |(< (/ x) 0)|))
 (2 2 (:REWRITE |(< (* x y) 0)|))
 (2 2 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:META META-INTEGERP-CORRECT))
 (2 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (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 NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (1 1 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1 1 (:REWRITE DEFAULT-MINUS))
 (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 |(< (+ c/d x) y)|))
 (1 1 (:REWRITE |(< (+ (- c) x) y)|))
 (1 1 (:META META-RATIONALP-CORRECT))
 )
(M1::THEOREM-A
 (75852 98 (:DEFINITION M1::TM-TO-TM1))
 (55766 3348 (:REWRITE DEFAULT-CDR))
 (53988 608 (:REWRITE M1::CONSP-ASSOC))
 (50868 628 (:REWRITE M1::NAT-TO-NAT-ALISTP-TO-ALISTP))
 (48984 628 (:DEFINITION M1::NAT-TO-NAT-ALISTP))
 (27318 314 (:DEFINITION ALISTP))
 (26928 68 (:DEFINITION M1::MAX-WIDTH1))
 (19671 618 (:DEFINITION ASSOC-EQUAL))
 (16199 2849 (:REWRITE ACL2-NUMBERP-X))
 (15723 1321 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12512 136 (:DEFINITION M1::LOG2))
 (12308 136 (:DEFINITION MAX))
 (5673 5673 (:REWRITE DEFAULT-CAR))
 (5100 68 (:REWRITE |(< x (if a b c))|))
 (4450 1108 (:REWRITE RATIONALP-X))
 (4450 1108 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (3876 3876 (:TYPE-PRESCRIPTION M1::LOG2))
 (3826 3826 (:REWRITE REDUCE-INTEGERP-+))
 (3826 3826 (:REWRITE INTEGERP-MINUS-X))
 (3826 3826 (:META META-INTEGERP-CORRECT))
 (3720 24 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (3648 24 (:DEFINITION M1::HALF-TAPE))
 (3400 136 (:REWRITE |(floor x 2)| . 1))
 (3140 3140 (:TYPE-PRESCRIPTION M1::NAT-TO-NAT-ALISTP))
 (2516 68 (:REWRITE M1::LOG2-IMPLIES-EXPT-UPPERBOUND))
 (2469 1321 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2055 1696 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2055 1696 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2048 1764 (:REWRITE DEFAULT-LESS-THAN-1))
 (2044 1696 (:REWRITE SIMPLIFY-SUMS-<))
 (1998 1321 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1908 12 (:DEFINITION TRUE-LISTP))
 (1768 1768 (:REWRITE THE-FLOOR-BELOW))
 (1768 1768 (:REWRITE THE-FLOOR-ABOVE))
 (1702 1696 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (1696 1696 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (1696 1696 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (1696 1696 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (1696 1696 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (1696 1696 (:REWRITE INTEGERP-<-CONSTANT))
 (1696 1696 (:REWRITE CONSTANT-<-INTEGERP))
 (1696 1696 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (1696 1696 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (1696 1696 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (1696 1696 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (1696 1696 (:REWRITE |(< c (- x))|))
 (1696 1696 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (1696 1696 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (1696 1696 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (1696 1696 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (1696 1696 (:REWRITE |(< (/ x) (/ y))|))
 (1696 1696 (:REWRITE |(< (- x) c)|))
 (1696 1696 (:REWRITE |(< (- x) (- y))|))
 (1496 136 (:REWRITE DEFAULT-FLOOR-RATIO))
 (1341 1341 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (1341 1341 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (1341 1341 (:REWRITE |(< (/ x) 0)|))
 (1341 1341 (:REWRITE |(< (* x y) 0)|))
 (1321 1321 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (1321 1321 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (1321 1321 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (1321 1321 (:REWRITE |(equal c (/ x))|))
 (1321 1321 (:REWRITE |(equal c (- x))|))
 (1321 1321 (:REWRITE |(equal (/ x) c)|))
 (1321 1321 (:REWRITE |(equal (/ x) (/ y))|))
 (1321 1321 (:REWRITE |(equal (- x) c)|))
 (1321 1321 (:REWRITE |(equal (- x) (- y))|))
 (1200 21 (:DEFINITION M1::INSTR))
 (1187 495 (:REWRITE DEFAULT-PLUS-2))
 (1108 1108 (:REWRITE REDUCE-RATIONALP-+))
 (1108 1108 (:REWRITE REDUCE-RATIONALP-*))
 (1108 1108 (:REWRITE RATIONALP-MINUS-X))
 (1108 1108 (:META META-RATIONALP-CORRECT))
 (1088 68 (:REWRITE |(+ x (if a b c))|))
 (680 680 (:REWRITE DEFAULT-TIMES-2))
 (680 680 (:REWRITE DEFAULT-TIMES-1))
 (544 544 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (544 136 (:REWRITE |(* y x)|))
 (495 495 (:REWRITE DEFAULT-PLUS-1))
 (427 427 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (427 427 (:REWRITE NORMALIZE-ADDENDS))
 (408 408 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (408 408 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (408 408 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (408 408 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (388 24 (:REWRITE M1::M1-STAYS-HALTED))
 (288 288 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (288 288 (:REWRITE M1::MEMBER-SUBSETP))
 (210 150 (:TYPE-PRESCRIPTION M1::NATP-CURRENT-SYM))
 (150 30 (:DEFINITION M1::NCODE))
 (143 143 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-REMAINDER))
 (143 143 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-AX+BX-RATIONAL-COMMON))
 (143 143 (:REWRITE |(< 0 (/ x))|))
 (143 143 (:REWRITE |(< 0 (* x y))|))
 (136 136 (:REWRITE DEFAULT-FLOOR-2))
 (136 136 (:REWRITE DEFAULT-FLOOR-1))
 (136 136 (:REWRITE |(floor x 2)| . 2))
 (136 136 (:REWRITE |(< y (+ (- c) x))|))
 (136 136 (:REWRITE |(< x (+ c/d y))|))
 (128 128 (:TYPE-PRESCRIPTION M1::TMI))
 (120 120 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (96 96 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (96 96 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (84 12 (:DEFINITION LEN))
 (68 68 (:TYPE-PRESCRIPTION NATP))
 (43 43 (:TYPE-PRESCRIPTION M1::NATP-CDR-ASSOC-MAP))
 (3 3 (:LINEAR M1::K-NON-0))
 )
(M1::DOWN
 (12 6 (:TYPE-PRESCRIPTION M1::NATP-CDR-ASSOC-MAP))
 (6 6 (:TYPE-PRESCRIPTION M1::NATP-MAP))
 )
(M1::UP)
(M1::A
 (3096 4 (:DEFINITION M1::TM-TO-TM1))
 (2498 162 (:REWRITE DEFAULT-CDR))
 (2406 26 (:REWRITE M1::CONSP-ASSOC))
 (2268 28 (:REWRITE M1::NAT-TO-NAT-ALISTP-TO-ALISTP))
 (2184 28 (:DEFINITION M1::NAT-TO-NAT-ALISTP))
 (1218 14 (:DEFINITION ALISTP))
 (1119 183 (:REWRITE ACL2-NUMBERP-X))
 (1116 97 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (802 26 (:DEFINITION ASSOC-EQUAL))
 (792 2 (:DEFINITION M1::MAX-WIDTH1))
 (620 4 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (608 4 (:DEFINITION M1::HALF-TAPE))
 (368 4 (:DEFINITION M1::LOG2))
 (362 4 (:DEFINITION MAX))
 (318 2 (:DEFINITION TRUE-LISTP))
 (312 78 (:REWRITE RATIONALP-X))
 (312 78 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (297 297 (:REWRITE DEFAULT-CAR))
 (223 223 (:REWRITE REDUCE-INTEGERP-+))
 (223 223 (:REWRITE INTEGERP-MINUS-X))
 (223 223 (:META META-INTEGERP-CORRECT))
 (180 97 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (150 3 (:DEFINITION M1::INSTR))
 (150 2 (:REWRITE |(< x (if a b c))|))
 (140 140 (:TYPE-PRESCRIPTION M1::NAT-TO-NAT-ALISTP))
 (127 97 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (114 114 (:TYPE-PRESCRIPTION M1::LOG2))
 (100 4 (:REWRITE |(floor x 2)| . 1))
 (97 97 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (97 97 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (97 97 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (97 97 (:REWRITE |(equal c (/ x))|))
 (97 97 (:REWRITE |(equal c (- x))|))
 (97 97 (:REWRITE |(equal (/ x) c)|))
 (97 97 (:REWRITE |(equal (/ x) (/ y))|))
 (97 97 (:REWRITE |(equal (- x) c)|))
 (97 97 (:REWRITE |(equal (- x) (- y))|))
 (91 72 (:REWRITE DEFAULT-LESS-THAN-2))
 (81 70 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (81 70 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (80 72 (:REWRITE DEFAULT-LESS-THAN-1))
 (80 70 (:REWRITE SIMPLIFY-SUMS-<))
 (78 78 (:REWRITE REDUCE-RATIONALP-+))
 (78 78 (:REWRITE REDUCE-RATIONALP-*))
 (78 78 (:REWRITE RATIONALP-MINUS-X))
 (78 78 (:META META-RATIONALP-CORRECT))
 (74 2 (:REWRITE M1::LOG2-IMPLIES-EXPT-UPPERBOUND))
 (72 72 (:REWRITE THE-FLOOR-BELOW))
 (72 72 (:REWRITE THE-FLOOR-ABOVE))
 (70 70 (:TYPE-PRESCRIPTION ALISTP))
 (70 70 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (70 70 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (70 70 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (70 70 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (70 70 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (70 70 (:REWRITE INTEGERP-<-CONSTANT))
 (70 70 (:REWRITE CONSTANT-<-INTEGERP))
 (70 70 (:REWRITE |(< c (/ x)) positive c --- present in goal|))
 (70 70 (:REWRITE |(< c (/ x)) positive c --- obj t or nil|))
 (70 70 (:REWRITE |(< c (/ x)) negative c --- present in goal|))
 (70 70 (:REWRITE |(< c (/ x)) negative c --- obj t or nil|))
 (70 70 (:REWRITE |(< c (- x))|))
 (70 70 (:REWRITE |(< (/ x) c) positive c --- present in goal|))
 (70 70 (:REWRITE |(< (/ x) c) positive c --- obj t or nil|))
 (70 70 (:REWRITE |(< (/ x) c) negative c --- present in goal|))
 (70 70 (:REWRITE |(< (/ x) c) negative c --- obj t or nil|))
 (70 70 (:REWRITE |(< (/ x) (/ y))|))
 (70 70 (:REWRITE |(< (- x) c)|))
 (70 70 (:REWRITE |(< (- x) (- y))|))
 (59 59 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-REMAINDER))
 (59 59 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-<-0-RATIONAL-COMMON))
 (59 59 (:REWRITE |(< (/ x) 0)|))
 (59 59 (:REWRITE |(< (* x y) 0)|))
 (54 2 (:REWRITE M1::M1-STAYS-HALTED))
 (48 48 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (48 48 (:REWRITE M1::MEMBER-SUBSETP))
 (44 4 (:REWRITE DEFAULT-FLOOR-RATIO))
 (41 41 (:TYPE-PRESCRIPTION M1::TMI))
 (39 17 (:REWRITE DEFAULT-PLUS-2))
 (32 2 (:REWRITE |(+ x (if a b c))|))
 (20 20 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (20 20 (:REWRITE DEFAULT-TIMES-2))
 (20 20 (:REWRITE DEFAULT-TIMES-1))
 (17 17 (:REWRITE DEFAULT-PLUS-1))
 (16 16 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (16 16 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (16 16 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (16 4 (:REWRITE |(* y x)|))
 (15 15 (:TYPE-PRESCRIPTION M1::NATP-CURRENT-SYM))
 (15 15 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (15 15 (:REWRITE NORMALIZE-ADDENDS))
 (14 2 (:DEFINITION LEN))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (12 12 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (11 11 (:TYPE-PRESCRIPTION M1::NATP-CDR-ASSOC-MAP))
 (10 2 (:DEFINITION M1::NCODE))
 (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))|))
 (4 4 (:REWRITE DEFAULT-FLOOR-2))
 (4 4 (:REWRITE DEFAULT-FLOOR-1))
 (4 4 (:REWRITE |(floor x 2)| . 2))
 (4 4 (:REWRITE |(< y (+ (- c) x))|))
 (4 4 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 )
(M1::B
 (1548 2 (:DEFINITION M1::TM-TO-TM1))
 (1270 102 (:REWRITE DEFAULT-CDR))
 (1203 13 (:REWRITE M1::CONSP-ASSOC))
 (1134 14 (:REWRITE M1::NAT-TO-NAT-ALISTP-TO-ALISTP))
 (1092 14 (:DEFINITION M1::NAT-TO-NAT-ALISTP))
 (986 29 (:DEFINITION NATP))
 (732 1 (:DEFINITION M1::TURING-MACHINEP))
 (728 1 (:DEFINITION M1::TURING-4-TUPLE))
 (719 69 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (710 122 (:REWRITE ACL2-NUMBERP-X))
 (670 14 (:DEFINITION MEMBER-EQUAL))
 (609 7 (:DEFINITION ALISTP))
 (600 12 (:DEFINITION M1::INSTR))
 (428 3 (:DEFINITION M1::SYMP))
 (401 13 (:DEFINITION ASSOC-EQUAL))
 (396 1 (:DEFINITION M1::MAX-WIDTH1))
 (310 2 (:REWRITE M1::HALF-TAPE-IMPLIES-TRUE-LISTP))
 (304 2 (:DEFINITION M1::HALF-TAPE))
 (254 1 (:DEFINITION M1::OPERATIONP))
 (196 49 (:REWRITE RATIONALP-X))
 (196 49 (:REWRITE M1::INTEGERP-IMPLIES-RATIONALP))
 (184 2 (:DEFINITION M1::LOG2))
 (181 2 (:DEFINITION MAX))
 (180 180 (:REWRITE DEFAULT-CAR))
 (159 1 (:DEFINITION TRUE-LISTP))
 (131 131 (:REWRITE REDUCE-INTEGERP-+))
 (131 131 (:REWRITE INTEGERP-MINUS-X))
 (131 131 (:META META-INTEGERP-CORRECT))
 (131 69 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (105 69 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (75 1 (:REWRITE |(< x (if a b c))|))
 (74 6 (:REWRITE ZP-OPEN))
 (70 70 (:TYPE-PRESCRIPTION M1::NAT-TO-NAT-ALISTP))
 (69 69 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-EQUAL))
 (69 69 (:REWRITE REDUCE-ADDITIVE-CONSTANT-EQUAL))
 (69 69 (:REWRITE EQUAL-OF-PREDICATES-REWRITE))
 (69 69 (:REWRITE |(equal c (/ x))|))
 (69 69 (:REWRITE |(equal c (- x))|))
 (69 69 (:REWRITE |(equal (/ x) c)|))
 (69 69 (:REWRITE |(equal (/ x) (/ y))|))
 (69 69 (:REWRITE |(equal (- x) c)|))
 (69 69 (:REWRITE |(equal (- x) (- y))|))
 (60 60 (:TYPE-PRESCRIPTION M1::NATP-CURRENT-SYM))
 (57 57 (:TYPE-PRESCRIPTION M1::LOG2))
 (50 2 (:REWRITE |(floor x 2)| . 1))
 (49 49 (:REWRITE REDUCE-RATIONALP-+))
 (49 49 (:REWRITE REDUCE-RATIONALP-*))
 (49 49 (:REWRITE RATIONALP-MINUS-X))
 (49 49 (:META META-RATIONALP-CORRECT))
 (44 44 (:TYPE-PRESCRIPTION M1::TMI))
 (44 35 (:REWRITE DEFAULT-LESS-THAN-2))
 (39 35 (:REWRITE DEFAULT-LESS-THAN-1))
 (39 34 (:REWRITE SIMPLIFY-SUMS-<))
 (39 34 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (39 34 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (37 1 (:REWRITE M1::LOG2-IMPLIES-EXPT-UPPERBOUND))
 (35 35 (:TYPE-PRESCRIPTION ALISTP))
 (35 35 (:REWRITE THE-FLOOR-BELOW))
 (35 35 (:REWRITE THE-FLOOR-ABOVE))
 (34 34 (:REWRITE REMOVE-WEAK-INEQUALITIES))
 (34 34 (:REWRITE REMOVE-STRICT-INEQUALITIES))
 (34 34 (:REWRITE REDUCE-RATIONAL-MULTIPLICATIVE-CONSTANT-<))
 (34 34 (:REWRITE REDUCE-MULTIPLICATIVE-CONSTANT-<))
 (34 34 (:REWRITE REDUCE-ADDITIVE-CONSTANT-<))
 (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))|))
 (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)|))
 (27 1 (:REWRITE M1::M1-STAYS-HALTED))
 (24 24 (:REWRITE M1::SUBSETP-IMPLIES-MEMBER))
 (24 24 (:REWRITE M1::MEMBER-SUBSETP))
 (23 12 (:REWRITE DEFAULT-PLUS-2))
 (22 2 (:REWRITE DEFAULT-FLOOR-RATIO))
 (16 1 (:REWRITE |(+ x (if a b c))|))
 (15 15 (:TYPE-PRESCRIPTION M1::MAX-WIDTH1))
 (12 12 (:REWRITE DEFAULT-PLUS-1))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:TYPE-PRESCRIPTION M1::HALF-TAPE))
 (10 10 (:REWRITE DEFAULT-TIMES-2))
 (10 10 (:REWRITE DEFAULT-TIMES-1))
 (8 8 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (8 8 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-AX+BX-=-0))
 (8 8 (:REWRITE NORMALIZE-FACTORS-GATHER-EXPONENTS))
 (8 2 (:REWRITE |(* y x)|))
 (7 1 (:DEFINITION LEN))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-4A))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-3A))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-2A))
 (6 6 (:TYPE-PRESCRIPTION NOT-INTEGERP-1A))
 (6 6 (:TYPE-PRESCRIPTION LEN))
 (5 1 (:DEFINITION M1::NCODE))
 (4 4 (:TYPE-PRESCRIPTION M1::TM-TO-TM1))
 (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 DEFAULT-FLOOR-2))
 (2 2 (:REWRITE DEFAULT-FLOOR-1))
 (2 2 (:REWRITE |(floor x 2)| . 2))
 (2 2 (:REWRITE |(< y (+ (- c) x))|))
 (2 2 (:REWRITE |(< x (+ c/d y))|))
 (2 2 (:REWRITE |(< 0 (/ x))|))
 (2 2 (:REWRITE |(< 0 (* x y))|))
 (2 2 (:DEFINITION M1::STATE-NAMEP))
 (1 1 (:TYPE-PRESCRIPTION NATP))
 )
