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 (120 12 (:DEFINITION LENGTH))
 (110 110 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
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 (72 59 (:REWRITE DEFAULT-CAR))
 (66 52 (:REWRITE DEFAULT-CDR))
 (48 48 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 2))
 (48 48 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
 (48 48 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 2))
 (48 48 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
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 (41 41 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
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 (36 36 (:REWRITE |(< (- x) 0)|))
 (34 34 (:REWRITE FOLD-CONSTS-IN-+))
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 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
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 (12 12 (:REWRITE DEFAULT-REALPART))
 (12 12 (:REWRITE DEFAULT-NUMERATOR))
 (12 12 (:REWRITE DEFAULT-IMAGPART))
 (12 12 (:REWRITE DEFAULT-DENOMINATOR))
 (12 12 (:REWRITE DEFAULT-COERCE-2))
 (12 12 (:REWRITE DEFAULT-COERCE-1))
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 (8 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (8 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7 2 (:REWRITE |(equal (+ d x) (+ c y))|))
 (7 2 (:REWRITE |(< (+ d x) (+ c y))|))
 (5 2 (:REWRITE |(equal (+ c x) d)|))
 (4 2 (:REWRITE |(< d (+ c x y))|))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (2 1 (:REWRITE |(equal (+ c x y) d)|))
 (2 1 (:REWRITE |(< (+ c x) d)|))
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(SUBTREE-P-WHEN-NOT-EQUAL
 (10 2 (:DEFINITION PROPER-SUBTREEP))
 (4 4 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(PROPER-SUBTREEP-WHEN-NOT-CONSP)
(PROPER-SUBTREEP-OF-CONS
 (70 14 (:REWRITE SUBTREE-P-WHEN-NOT-EQUAL))
 (20 20 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (20 20 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (20 20 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (20 20 (:REWRITE |(equal (- x) (- y))|))
 (17 17 (:REWRITE PROPER-SUBTREEP-WHEN-NOT-CONSP))
 (11 11 (:REWRITE DEFAULT-CAR))
 (7 7 (:REWRITE DEFAULT-CDR))
 )
(HAS-PROPER-SUBTREE-IN-LIST)
(HAS-PROPER-SUBTREE-IN-LIST-WHEN-NOT-CONSP)
(HAS-PROPER-SUBTREE-IN-LIST-OF-CONSP
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 (6 6 (:REWRITE HAS-PROPER-SUBTREE-IN-LIST-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(NON-SUBTREE-LISTP)
(NON-SUBTREE-LISTP-WHEN-NOT-CONSP)
(NON-SUBTREE-LISTP-OF-CONSP
 (6 6 (:REWRITE NON-SUBTREE-LISTP-WHEN-NOT-CONSP))
 (5 5 (:REWRITE HAS-PROPER-SUBTREE-IN-LIST-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(TIP-P)
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 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(TIP-P-OF-CONS)
(TIP-LISTP)
(TIP-LISTP-WHEN-NOT-CONSP)
(TIP-LISTP-OF-CONSP
 (6 6 (:REWRITE TIP-LISTP-WHEN-NOT-CONSP))
 (5 5 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
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(TREEP
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 (190 10 (:REWRITE |(+ (if a b c) x)|))
 (129 100 (:REWRITE DEFAULT-+-1))
 (110 10 (:REWRITE NUMERATOR-NEGATIVE))
 (100 100 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (100 10 (:DEFINITION LENGTH))
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 (70 10 (:DEFINITION LEN))
 (68 24 (:REWRITE DEFAULT-UNARY-MINUS))
 (65 51 (:REWRITE DEFAULT-CDR))
 (40 40 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 2))
 (40 40 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
 (40 40 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 2))
 (40 40 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
 (35 35 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (35 35 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (33 33 (:REWRITE |(< (- x) (- y))|))
 (32 32 (:REWRITE FOLD-CONSTS-IN-+))
 (30 30 (:REWRITE |(< (- x) 0)|))
 (29 23 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (29 23 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (24 22 (:REWRITE DEFAULT-<-2))
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 (20 20 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
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 (10 10 (:REWRITE DEFAULT-REALPART))
 (10 10 (:REWRITE DEFAULT-NUMERATOR))
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 (10 10 (:REWRITE DEFAULT-COERCE-2))
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 (10 10 (:META META-INTEGERP-CORRECT))
 (7 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (7 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7 2 (:REWRITE |(equal (+ d x) (+ c y))|))
 (7 2 (:REWRITE |(< (+ d x) (+ c y))|))
 (5 2 (:REWRITE |(equal (+ c x) d)|))
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 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (2 1 (:REWRITE |(equal (+ c x y) d)|))
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(TREEP-WHEN-NOT-CONSP
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 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
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(TREEP-OF-CONSP
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 (9 9 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE DEFAULT-CAR))
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(TREE-LISTP-WHEN-NOT-CONSP)
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 (5 5 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
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(TASPIP
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 (304 16 (:REWRITE |(+ (if a b c) x)|))
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 (160 16 (:DEFINITION LENGTH))
 (153 153 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (112 16 (:DEFINITION LEN))
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 (64 64 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 2))
 (64 64 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
 (64 64 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 2))
 (64 64 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
 (64 64 (:REWRITE DEFAULT-CAR))
 (57 57 (:REWRITE DEFAULT-CDR))
 (56 56 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (56 56 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (53 53 (:REWRITE |(< (- x) (- y))|))
 (48 48 (:REWRITE |(< (- x) 0)|))
 (47 47 (:REWRITE FOLD-CONSTS-IN-+))
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 (40 36 (:REWRITE DEFAULT-<-2))
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 (32 32 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (16 16 (:TYPE-PRESCRIPTION LEN))
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 (16 16 (:REWRITE DEFAULT-REALPART))
 (16 16 (:REWRITE DEFAULT-NUMERATOR))
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 (16 16 (:REWRITE DEFAULT-COERCE-1))
 (16 16 (:META META-INTEGERP-CORRECT))
 (10 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (10 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (10 3 (:REWRITE |(equal (+ d x) (+ c y))|))
 (7 3 (:REWRITE |(equal (+ c x) d)|))
 (7 2 (:REWRITE |(< (+ d x) (+ c y))|))
 (4 2 (:REWRITE |(< d (+ c x y))|))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (2 1 (:REWRITE |(equal (+ c x y) d)|))
 (2 1 (:REWRITE |(< (+ c x) d)|))
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(TASPIP-WHEN-NOT-CONSP
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
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(TASPIP-OF-CONS
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 (8 8 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:META META-INTEGERP-CORRECT))
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(TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG
 (5 5 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
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(TASPIP-FLG-AND-FLG-OPEN
 (2 2 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
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(TIP-P-GIVES-TASPIP-T
 (10 4 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (1 1 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:META META-INTEGERP-CORRECT))
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(COUNT-TIPS
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 (444 24 (:DEFINITION INTEGER-ABS))
 (340 116 (:REWRITE DEFAULT-+-2))
 (300 36 (:REWRITE |(+ y x)|))
 (228 12 (:REWRITE |(+ (if a b c) x)|))
 (152 116 (:REWRITE DEFAULT-+-1))
 (132 12 (:REWRITE NUMERATOR-NEGATIVE))
 (120 12 (:DEFINITION LENGTH))
 (116 116 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (116 116 (:REWRITE NORMALIZE-ADDENDS))
 (84 12 (:DEFINITION LEN))
 (75 63 (:REWRITE DEFAULT-CAR))
 (72 24 (:REWRITE DEFAULT-UNARY-MINUS))
 (71 59 (:REWRITE DEFAULT-CDR))
 (48 48 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 2))
 (48 48 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
 (48 48 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 2))
 (48 48 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
 (38 38 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (38 38 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (38 38 (:REWRITE |(< (- x) (- y))|))
 (36 36 (:REWRITE FOLD-CONSTS-IN-+))
 (36 36 (:REWRITE |(< (- x) 0)|))
 (36 36 (:REWRITE |(+ c (+ d x))|))
 (30 26 (:REWRITE SIMPLIFY-SUMS-<))
 (30 26 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (30 26 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (28 26 (:REWRITE DEFAULT-<-2))
 (28 26 (:REWRITE DEFAULT-<-1))
 (24 24 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (12 12 (:TYPE-PRESCRIPTION LEN))
 (12 12 (:REWRITE REDUCE-INTEGERP-+))
 (12 12 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (12 12 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (12 12 (:REWRITE INTEGERP-MINUS-X))
 (12 12 (:REWRITE DEFAULT-REALPART))
 (12 12 (:REWRITE DEFAULT-NUMERATOR))
 (12 12 (:REWRITE DEFAULT-IMAGPART))
 (12 12 (:REWRITE DEFAULT-DENOMINATOR))
 (12 12 (:REWRITE DEFAULT-COERCE-2))
 (12 12 (:REWRITE DEFAULT-COERCE-1))
 (12 12 (:META META-INTEGERP-CORRECT))
 (6 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (6 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (6 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6 2 (:REWRITE |(equal (+ d x) (+ c y))|))
 (6 2 (:REWRITE |(equal (+ c x) (+ d y))|))
 (6 2 (:REWRITE |(< (+ d x) (+ c y))|))
 (6 2 (:REWRITE |(< (+ c x) (+ d y))|))
 (4 2 (:REWRITE |(equal (+ c x) d)|))
 (4 2 (:REWRITE |(< d (+ c x))|))
 (4 2 (:REWRITE |(< (+ c x) d)|))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
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(COUNT-TIPS-WHEN-NOT-CONSP)
(COUNT-TIPS-OF-CONSP
 (20 10 (:REWRITE DEFAULT-+-2))
 (18 10 (:REWRITE DEFAULT-+-1))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (9 9 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE DEFAULT-CAR))
 )
(COUNT-TIPS-LIST-WHEN-NOT-CONSP)
(COUNT-TIPS-LIST-OF-CONSP
 (10 5 (:REWRITE DEFAULT-+-2))
 (10 5 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE COUNT-TIPS-LIST-WHEN-NOT-CONSP))
 (5 5 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (5 5 (:REWRITE NORMALIZE-ADDENDS))
 (5 5 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
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(TREES-WITH-N-TIPS)
(TREES-WITH-N-TIPS-WHEN-NOT-CONSP)
(TREES-WITH-N-TIPS-OF-CONSP
 (7 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (7 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (7 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (6 6 (:REWRITE TREES-WITH-N-TIPS-WHEN-NOT-CONSP))
 (5 5 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(ALL-SAME-NUM-TIPS)
(ALL-SAME-NUM-TIPS-WHEN-NOT-CONSP)
(ALL-SAME-NUM-TIPS-OF-CONSP
 (2 2 (:REWRITE TREES-WITH-N-TIPS-WHEN-NOT-CONSP))
 (2 2 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 (1 1 (:REWRITE ALL-SAME-NUM-TIPS-WHEN-NOT-CONSP))
 )
(NON-TIP-TREE-LISTP)
(NON-TIP-TREE-LISTP-WHEN-NOT-CONSP)
(NON-TIP-TREE-LISTP-OF-CONS
 (6 6 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-CDR))
 )
(MYTIPS
 (1 1 (:TYPE-PRESCRIPTION TRUE-LISTP))
 )
(MYTIPS-WHEN-NOT-CONSP)
(MYTIPS-OF-CONSP
 (35 7 (:DEFINITION BINARY-APPEND))
 (15 15 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (12 12 (:REWRITE DEFAULT-CDR))
 (12 12 (:REWRITE DEFAULT-CAR))
 )
(TRUE-LISTP-MYTIPS)
(FIRST-TAXON)
(FIRST-TAXON-WHEN-NOT-CONSP)
(FIRST-TAXON-OF-CONSP
 (6 6 (:REWRITE FIRST-TAXON-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(TIP-P-NOT-INTEGER-GIVES-SYMBOLP)
(TREEP-AND-CONSP-GIVES-TREE-LISTP
 (1 1 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE DEFAULT-CDR))
 )
(COUNT-TIPS-OF-CONSP-EQUAL-COUNT-TIPS-LIST
 (3 3 (:REWRITE COUNT-TIPS-LIST-WHEN-NOT-CONSP))
 (1 1 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 )
(TIP-P-GIVES-COUNT-TIPS-LIST-EQUAL-0
 (5 1 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (2 2 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:META META-INTEGERP-CORRECT))
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(TIP-P-NOT-PROPER-SUBTREE
 (5 1 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (2 2 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE REDUCE-INTEGERP-+))
 (1 1 (:REWRITE INTEGERP-MINUS-X))
 (1 1 (:META META-INTEGERP-CORRECT))
 )
(TREE-LIST-LISTP-TREE-LISTP
 (14 14 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (14 14 (:REWRITE DEFAULT-CAR))
 (8 8 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (3 3 (:REWRITE DEFAULT-CDR))
 )
(COUNT-TIPS-MIN
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 (31 16 (:REWRITE SIMPLIFY-SUMS-<))
 (31 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (31 16 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (31 16 (:REWRITE DEFAULT-<-1))
 (28 16 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (22 22 (:TYPE-PRESCRIPTION TIP-P))
 (16 16 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (16 16 (:REWRITE DEFAULT-<-2))
 (16 16 (:REWRITE |(< (- x) (- y))|))
 (15 15 (:REWRITE COUNT-TIPS-LIST-WHEN-NOT-CONSP))
 (11 11 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (9 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (9 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (9 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (7 7 (:REWRITE DEFAULT-CDR))
 (5 5 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (4 4 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (4 4 (:REWRITE |(equal (- x) 0)|))
 (4 4 (:REWRITE |(< (- x) 0)|))
 )
(COUNT-TIPS-LIST-SUBTREES
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 (867 323 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (688 349 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (600 150 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (592 321 (:REWRITE DEFAULT-<-2))
 (588 321 (:REWRITE DEFAULT-<-1))
 (367 367 (:REWRITE DEFAULT-CAR))
 (336 336 (:REWRITE |(< (- x) (- y))|))
 (300 300 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (237 237 (:REWRITE DEFAULT-CDR))
 (150 150 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (150 150 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (72 55 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (72 55 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (72 55 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (55 55 (:REWRITE |(equal (- x) (- y))|))
 (45 15 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (28 14 (:REWRITE DEFAULT-+-2))
 (26 26 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (26 26 (:REWRITE DEFAULT-UNARY-/))
 (20 14 (:REWRITE DEFAULT-+-1))
 (16 16 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (16 16 (:REWRITE COUNT-TIPS-OF-CONSP-EQUAL-COUNT-TIPS-LIST))
 (15 15 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (15 15 (:REWRITE REDUCE-INTEGERP-+))
 (15 15 (:REWRITE INTEGERP-MINUS-X))
 (15 15 (:REWRITE |(< 0 (- x))|))
 (15 15 (:META META-INTEGERP-CORRECT))
 (14 14 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (11 11 (:REWRITE |(equal (- x) 0)|))
 (9 9 (:REWRITE TIP-P-OF-CONS))
 (8 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (4 4 (:REWRITE |(+ c (+ d x))|))
 )
(PROPER-SUBTREE-GIVES-<-COUNT-TIPS
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 (112 8 (:DEFINITION PROPER-SUBTREEP))
 (92 46 (:REWRITE DEFAULT-+-2))
 (92 46 (:REWRITE DEFAULT-+-1))
 (80 20 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (72 72 (:REWRITE DEFAULT-CDR))
 (54 54 (:REWRITE DEFAULT-CAR))
 (52 52 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (50 25 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (46 46 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (46 46 (:REWRITE NORMALIZE-ADDENDS))
 (40 40 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (25 25 (:REWRITE REDUCE-INTEGERP-+))
 (25 25 (:REWRITE INTEGERP-MINUS-X))
 (25 25 (:META META-INTEGERP-CORRECT))
 (20 20 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (20 20 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (18 13 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (18 13 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (18 13 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (14 14 (:REWRITE PROPER-SUBTREEP-WHEN-NOT-CONSP))
 (13 13 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (13 13 (:REWRITE |(equal (- x) (- y))|))
 (10 10 (:TYPE-PRESCRIPTION SUBTREEP))
 (2 2 (:REWRITE TIP-P-OF-CONS))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (2 1 (:REWRITE SIMPLIFY-SUMS-<))
 (2 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE |(equal (- x) 0)|))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 )
(TREES-WITH-N-TIPS-NOT-HAS-PROPER-SUBTREE-IN-LIST
 (33 33 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (33 33 (:REWRITE COUNT-TIPS-OF-CONSP-EQUAL-COUNT-TIPS-LIST))
 (32 8 (:REWRITE TIP-P-NOT-PROPER-SUBTREE))
 (28 9 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (18 9 (:REWRITE DEFAULT-<-2))
 (16 16 (:TYPE-PRESCRIPTION TIP-P))
 (12 12 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (11 11 (:REWRITE HAS-PROPER-SUBTREE-IN-LIST-WHEN-NOT-CONSP))
 (11 9 (:REWRITE SIMPLIFY-SUMS-<))
 (11 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (11 9 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (10 10 (:REWRITE TREES-WITH-N-TIPS-WHEN-NOT-CONSP))
 (10 9 (:REWRITE DEFAULT-<-1))
 (9 9 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (9 9 (:REWRITE |(< (- x) (- y))|))
 (8 8 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (8 8 (:REWRITE PROPER-SUBTREEP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE PROPER-SUBTREE-GIVES-<-COUNT-TIPS))
 )
(TREES-WITH-N-TIPS-NON-SUBTREE-LISTP
 (335 84 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (171 171 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (171 171 (:REWRITE COUNT-TIPS-OF-CONSP-EQUAL-COUNT-TIPS-LIST))
 (163 163 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (134 134 (:REWRITE DEFAULT-CAR))
 (88 88 (:REWRITE DEFAULT-CDR))
 (88 84 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (57 15 (:REWRITE TIP-P-NOT-PROPER-SUBTREE))
 (52 52 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (28 28 (:TYPE-PRESCRIPTION TIP-P))
 (18 6 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (18 6 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (18 6 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (15 15 (:REWRITE PROPER-SUBTREEP-WHEN-NOT-CONSP))
 (14 14 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (6 6 (:REWRITE |(equal (- x) (- y))|))
 )
(ALL-SAME-NUM-TIPS-NON-SUBTREE-LISTP
 (141 33 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (66 66 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (44 44 (:REWRITE TREES-WITH-N-TIPS-WHEN-NOT-CONSP))
 (33 33 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (30 30 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (27 27 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (27 27 (:REWRITE COUNT-TIPS-OF-CONSP-EQUAL-COUNT-TIPS-LIST))
 (23 23 (:REWRITE DEFAULT-CAR))
 (15 6 (:REWRITE TIP-P-NOT-PROPER-SUBTREE))
 (15 3 (:REWRITE NON-TIP-TREE-LISTP-OF-CONS))
 (13 13 (:REWRITE ALL-SAME-NUM-TIPS-WHEN-NOT-CONSP))
 (12 12 (:REWRITE NON-SUBTREE-LISTP-WHEN-NOT-CONSP))
 (9 9 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (8 8 (:REWRITE HAS-PROPER-SUBTREE-IN-LIST-WHEN-NOT-CONSP))
 (6 6 (:TYPE-PRESCRIPTION TIP-P))
 (6 6 (:REWRITE PROPER-SUBTREEP-WHEN-NOT-CONSP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 )
(ALL-SAME-NUM-TIPS-ATOM)
(SUBTREEP-SELF
 (1 1 (:REWRITE SUBTREE-P-WHEN-NOT-EQUAL))
 )
(SUBTREEP-SMALLER
 (1554 84 (:DEFINITION INTEGER-ABS))
 (1063 350 (:REWRITE DEFAULT-+-2))
 (798 42 (:REWRITE |(+ (if a b c) x)|))
 (462 350 (:REWRITE DEFAULT-+-1))
 (462 42 (:REWRITE NUMERATOR-NEGATIVE))
 (420 42 (:DEFINITION LENGTH))
 (350 350 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (294 42 (:DEFINITION LEN))
 (256 86 (:REWRITE DEFAULT-UNARY-MINUS))
 (168 168 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 2))
 (168 168 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
 (168 168 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 2))
 (168 168 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
 (162 144 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (152 144 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (143 143 (:REWRITE |(< (- x) (- y))|))
 (132 100 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (126 126 (:REWRITE |(< (- x) 0)|))
 (119 99 (:REWRITE DEFAULT-<-1))
 (114 114 (:REWRITE |(+ c (+ d x))|))
 (111 111 (:REWRITE FOLD-CONSTS-IN-+))
 (108 99 (:REWRITE DEFAULT-<-2))
 (102 102 (:REWRITE DEFAULT-CDR))
 (91 23 (:REWRITE TIP-P-NOT-PROPER-SUBTREE))
 (84 84 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (60 60 (:REWRITE DEFAULT-CAR))
 (45 45 (:TYPE-PRESCRIPTION TIP-P))
 (42 42 (:TYPE-PRESCRIPTION LEN))
 (42 42 (:REWRITE REDUCE-INTEGERP-+))
 (42 42 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (42 42 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (42 42 (:REWRITE INTEGERP-MINUS-X))
 (42 42 (:REWRITE DEFAULT-REALPART))
 (42 42 (:REWRITE DEFAULT-NUMERATOR))
 (42 42 (:REWRITE DEFAULT-IMAGPART))
 (42 42 (:REWRITE DEFAULT-DENOMINATOR))
 (42 42 (:REWRITE DEFAULT-COERCE-2))
 (42 42 (:REWRITE DEFAULT-COERCE-1))
 (42 42 (:META META-INTEGERP-CORRECT))
 (22 22 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (22 22 (:REWRITE PROPER-SUBTREEP-WHEN-NOT-CONSP))
 (14 7 (:REWRITE |(< (+ c x y) d)|))
 (10 2 (:REWRITE SUBTREE-P-WHEN-NOT-EQUAL))
 (9 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (9 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (9 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8 8 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-1/AX+BX))
 (2 2 (:REWRITE DEFAULT-UNARY-/))
 (1 1 (:REWRITE TIP-P-OF-CONS))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (1 1 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (1 1 (:REWRITE |(equal (- x) 0)|))
 (1 1 (:REWRITE |(< 0 (- x))|))
 )
(NON-SUBTREE-LISTP-CDRS
 (1965 78 (:REWRITE TREES-WITH-N-TIPS-NON-SUBTREE-LISTP))
 (478 478 (:TYPE-PRESCRIPTION TREES-WITH-N-TIPS))
 (324 79 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (223 223 (:TYPE-PRESCRIPTION COUNT-TIPS))
 (187 187 (:TYPE-PRESCRIPTION TREE-LISTP))
 (156 156 (:REWRITE TREES-WITH-N-TIPS-WHEN-NOT-CONSP))
 (153 153 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (142 14 (:REWRITE TREES-WITH-N-TIPS-OF-CONSP))
 (131 131 (:REWRITE DEFAULT-CAR))
 (130 130 (:REWRITE COUNT-TIPS-WHEN-NOT-CONSP))
 (130 130 (:REWRITE COUNT-TIPS-OF-CONSP-EQUAL-COUNT-TIPS-LIST))
 (84 79 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (82 77 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (56 14 (:REWRITE TIP-P-NOT-PROPER-SUBTREE))
 (50 1 (:REWRITE |(equal (if a b c) x)|))
 (37 37 (:REWRITE TREES-WITH-N-TIPS-NOT-HAS-PROPER-SUBTREE-IN-LIST))
 (28 28 (:TYPE-PRESCRIPTION TIP-P))
 (20 8 (:LINEAR PROPER-SUBTREE-GIVES-<-COUNT-TIPS))
 (20 2 (:REWRITE TREE-LISTP-OF-CONSP))
 (19 4 (:LINEAR COUNT-TIPS-MIN))
 (16 16 (:TYPE-PRESCRIPTION TREEP))
 (14 14 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (14 14 (:REWRITE PROPER-SUBTREEP-WHEN-NOT-CONSP))
 (14 14 (:REWRITE CAR-CONS))
 (12 2 (:REWRITE NON-TIP-TREE-LISTP-OF-CONS))
 (10 10 (:DEFINITION NULL))
 (8 8 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (3 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (3 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(PROPER-GIVES-SUBTREE
 (8 2 (:REWRITE TIP-P-NOT-PROPER-SUBTREE))
 (5 1 (:REWRITE SUBTREE-P-WHEN-NOT-EQUAL))
 (4 4 (:TYPE-PRESCRIPTION TIP-P))
 (2 2 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE PROPER-SUBTREEP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 )
(TREE-LISTP-AND-CONSP-GIVES-TREEP
 (8 2 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (4 4 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (2 2 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (1 1 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 )
(TASPIP-FLG-AND-FLG-GIVES-T
 (19 5 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (3 3 (:REWRITE REDUCE-INTEGERP-+))
 (3 3 (:REWRITE INTEGERP-MINUS-X))
 (3 3 (:META META-INTEGERP-CORRECT))
 )
(TASPIP-FLG-CONSP-GIVES-TASPIP-NIL
 (14 6 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (6 6 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 )
