(GET-MIN-KEY
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 (600 42 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (571 28 (:REWRITE INTEGER-HALISTP-HALISTP))
 (538 269 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (497 32 (:DEFINITION INTEGER-HALISTP))
 (471 42 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (393 393 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (314 10 (:REWRITE ASSOC-HQUAL-FROM-MEMBER-GEN-STRIP-CARS))
 (215 23 (:REWRITE PERM-IMPLIES-SUBSET))
 (171 38 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (144 36 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (142 121 (:REWRITE DEFAULT-CDR))
 (137 43 (:REWRITE SUBSET-SAME-MEMBERS))
 (133 19 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (112 28 (:REWRITE PERM-WHEN-NOT-CONSP))
 (101 100 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (100 28 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (92 23 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (87 43 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (85 85 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (80 80 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (61 17 (:DEFINITION HONS-EQUAL))
 (56 56 (:TYPE-PRESCRIPTION PERM))
 (50 50 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (49 49 (:REWRITE REDUCE-INTEGERP-+))
 (49 49 (:REWRITE INTEGERP-MINUS-X))
 (49 49 (:META META-INTEGERP-CORRECT))
 (43 43 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (41 14 (:REWRITE SIMPLIFY-SUMS-<))
 (41 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (41 14 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (41 14 (:REWRITE DEFAULT-<-1))
 (36 36 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (36 36 (:REWRITE NOT-MEMBER-SUBSET))
 (27 9 (:REWRITE ASSOC-CAR-FROM-SUBSET))
 (26 14 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (24 24 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (23 23 (:REWRITE SUBSET-TRANSITIVE))
 (23 23 (:REWRITE SUBSET-APPEND-GIVES-2))
 (23 23 (:REWRITE SUBSET-APPEND-GIVES-1))
 (18 18 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (14 14 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (14 14 (:REWRITE DEFAULT-<-2))
 (14 14 (:REWRITE |(< (- x) (- y))|))
 (11 11 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (11 11 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (11 11 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (11 11 (:REWRITE |(equal (- x) (- y))|))
 (9 9 (:REWRITE MEMBER-GIVES-ASSOC-HQUAL))
 )
(GET-MIN-KEY-WHEN-NOT-CONSP)
(GET-MIN-KEY-OF-CONSP
 (368 8 (:DEFINITION HONS-ASSOC-EQUAL))
 (312 24 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (262 131 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (131 131 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (131 131 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (98 7 (:REWRITE SIMPLIFY-SUMS-<))
 (98 7 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (98 7 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (98 7 (:REWRITE DEFAULT-<-1))
 (96 24 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (96 24 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (72 72 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (58 34 (:REWRITE DEFAULT-CDR))
 (57 57 (:REWRITE DEFAULT-CAR))
 (48 48 (:TYPE-PRESCRIPTION MEMBER-GEN))
 (48 48 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (40 8 (:DEFINITION HONS-EQUAL))
 (33 7 (:REWRITE DEFAULT-<-2))
 (30 30 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (24 24 (:REWRITE SUBSET-SAME-MEMBERS))
 (24 24 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (24 24 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (24 24 (:REWRITE NOT-MEMBER-SUBSET))
 (24 24 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (24 24 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (24 24 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (15 15 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (8 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (8 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8 8 (:REWRITE |(equal (- x) (- y))|))
 (7 7 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (7 7 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (7 7 (:REWRITE |(< (- x) (- y))|))
 )
(GREATER-ALL
 (10 10 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 )
(GREATER-ALL-WHEN-NOT-CONSP)
(GREATER-ALL-OF-CONSP
 (8 8 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (5 5 (:REWRITE SIMPLIFY-SUMS-<))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (5 5 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (5 5 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (5 5 (:REWRITE DEFAULT-<-2))
 (5 5 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE DEFAULT-CAR))
 )
(MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN
 (4262 2131 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (2131 2131 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (1130 137 (:REWRITE SUBSET-SAME-MEMBERS))
 (595 140 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (582 162 (:REWRITE PERM-WHEN-NOT-CONSP))
 (501 501 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (464 116 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (404 104 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (370 64 (:REWRITE SIMPLIFY-SUMS-<))
 (370 64 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (370 64 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (324 324 (:TYPE-PRESCRIPTION PERM))
 (248 62 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (190 64 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (137 137 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (124 124 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (122 122 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (110 110 (:REWRITE SUBSET-TRANSITIVE))
 (110 110 (:REWRITE SUBSET-APPEND-GIVES-2))
 (110 110 (:REWRITE SUBSET-APPEND-GIVES-1))
 (90 6 (:REWRITE PERM-OF-CONSP))
 (72 6 (:REWRITE SUBSET-OF-CONSP))
 (64 64 (:REWRITE DEFAULT-<-2))
 (64 64 (:REWRITE |(< (- x) (- y))|))
 (62 62 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (44 24 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (24 6 (:REWRITE DEL-WHEN-NOT-CONSP))
 (22 22 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-0-<-A+AB))
 (22 22 (:REWRITE |(< 0 (- x))|))
 (14 14 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (14 14 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (14 14 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (14 14 (:REWRITE |(equal (- x) (- y))|))
 )
(GET-MIN-KEY-NOT-KEY-MEMBER-STRIP
 (1970 985 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (1872 42 (:DEFINITION HONS-ASSOC-EQUAL))
 (1638 126 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (985 985 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (576 144 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (544 540 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (504 126 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (282 25 (:REWRITE SIMPLIFY-SUMS-<))
 (282 25 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (282 25 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (282 25 (:REWRITE DEFAULT-<-1))
 (260 134 (:REWRITE DEFAULT-CDR))
 (252 252 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (238 34 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (178 178 (:REWRITE SUBSET-SAME-MEMBERS))
 (178 178 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (150 42 (:DEFINITION HONS-EQUAL))
 (148 148 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (146 146 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (144 144 (:REWRITE NOT-MEMBER-SUBSET))
 (126 126 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (51 51 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (51 51 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (51 51 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (51 51 (:REWRITE |(equal (- x) (- y))|))
 (34 34 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (32 32 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (25 25 (:REWRITE DEFAULT-<-2))
 (25 25 (:REWRITE |(< (- x) (- y))|))
 )
(GREATER-ALL-GIVES-MEMBER-KEY
 (3395 135 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (3130 45 (:DEFINITION HONS-ASSOC-EQUAL))
 (2598 1299 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (1305 185 (:REWRITE SUBSET-SAME-MEMBERS))
 (1299 1299 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (966 959 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (829 88 (:REWRITE PERM-IMPLIES-SUBSET))
 (705 185 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (664 166 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (595 148 (:REWRITE PERM-WHEN-NOT-CONSP))
 (540 135 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (393 393 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (363 228 (:REWRITE DEFAULT-CDR))
 (293 293 (:TYPE-PRESCRIPTION PERM))
 (270 270 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (246 19 (:REWRITE SIMPLIFY-SUMS-<))
 (246 19 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (246 19 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (246 19 (:REWRITE DEFAULT-<-1))
 (203 203 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (185 185 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (166 166 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (166 166 (:REWRITE NOT-MEMBER-SUBSET))
 (165 45 (:DEFINITION HONS-EQUAL))
 (135 135 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (88 88 (:REWRITE SUBSET-TRANSITIVE))
 (88 88 (:REWRITE SUBSET-APPEND-GIVES-2))
 (88 88 (:REWRITE SUBSET-APPEND-GIVES-1))
 (83 19 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (67 19 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (56 56 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (54 54 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (54 54 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (54 54 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (54 54 (:REWRITE |(equal (- x) (- y))|))
 (28 28 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (28 28 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (19 19 (:REWRITE DEFAULT-<-2))
 (19 19 (:REWRITE |(< (- x) (- y))|))
 )
(SORT-THE-ALIST-BY-INSERTION
 (124 2 (:DEFINITION ACL2-COUNT))
 (42 3 (:REWRITE INTEGER-HALISTP-HALISTP))
 (37 2 (:DEFINITION INTEGER-ABS))
 (33 3 (:DEFINITION INTEGER-HALISTP))
 (27 9 (:REWRITE DEFAULT-+-2))
 (25 3 (:REWRITE |(+ y x)|))
 (19 1 (:REWRITE |(+ (if a b c) x)|))
 (18 2 (:REWRITE PERM-IMPLIES-SUBSET))
 (15 15 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (12 9 (:REWRITE DEFAULT-+-1))
 (12 3 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (11 1 (:REWRITE NUMERATOR-NEGATIVE))
 (10 1 (:DEFINITION LENGTH))
 (9 9 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (9 9 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (9 9 (:REWRITE NORMALIZE-ADDENDS))
 (9 9 (:REWRITE DEFAULT-CDR))
 (8 8 (:REWRITE DEFAULT-CAR))
 (8 2 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (8 2 (:REWRITE PERM-WHEN-NOT-CONSP))
 (8 2 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (7 1 (:DEFINITION LEN))
 (6 6 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (6 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (5 5 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (4 4 (:TYPE-PRESCRIPTION PERM))
 (4 4 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 2))
 (4 4 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
 (4 4 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 2))
 (4 4 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (4 4 (:META META-INTEGERP-CORRECT))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (3 3 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (3 3 (:REWRITE FOLD-CONSTS-IN-+))
 (3 3 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (3 3 (:REWRITE |(< (- x) 0)|))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (3 3 (:REWRITE |(+ c (+ d x))|))
 (2 2 (:REWRITE SUBSET-TRANSITIVE))
 (2 2 (:REWRITE SUBSET-SAME-MEMBERS))
 (2 2 (:REWRITE SUBSET-APPEND-GIVES-2))
 (2 2 (:REWRITE SUBSET-APPEND-GIVES-1))
 (2 2 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE NOT-MEMBER-SUBSET))
 (2 2 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (2 2 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (2 2 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (2 2 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (1 1 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (1 1 (:REWRITE DEFAULT-REALPART))
 (1 1 (:REWRITE DEFAULT-NUMERATOR))
 (1 1 (:REWRITE DEFAULT-IMAGPART))
 (1 1 (:REWRITE DEFAULT-DENOMINATOR))
 (1 1 (:REWRITE DEFAULT-COERCE-2))
 (1 1 (:REWRITE DEFAULT-COERCE-1))
 )
(SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP)
(SORT-THE-ALIST-BY-INSERTION-OF-CONSP
 (368 8 (:DEFINITION HONS-ASSOC-EQUAL))
 (246 24 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (112 8 (:REWRITE INTEGER-HALISTP-HALISTP))
 (92 23 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (90 24 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (88 8 (:DEFINITION INTEGER-HALISTP))
 (54 54 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (48 48 (:REWRITE DEFAULT-CAR))
 (40 40 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (40 8 (:DEFINITION HONS-EQUAL))
 (39 39 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (32 32 (:REWRITE DEFAULT-CDR))
 (32 8 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (28 7 (:REWRITE PERM-WHEN-NOT-CONSP))
 (25 25 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (24 6 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (23 23 (:REWRITE SUBSET-SAME-MEMBERS))
 (23 23 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (20 20 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (18 6 (:REWRITE GREATER-ALL-GIVES-MEMBER-KEY))
 (15 15 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (14 14 (:TYPE-PRESCRIPTION PERM))
 (13 13 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (10 10 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (10 9 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (10 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (10 9 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (9 9 (:REWRITE |(equal (- x) (- y))|))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (8 8 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (8 8 (:META META-INTEGERP-CORRECT))
 (7 7 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (6 6 (:REWRITE SUBSET-THROUGH-DEL-PAIR))
 (6 6 (:REWRITE SUBSET-APPEND-GIVES-2))
 (6 6 (:REWRITE SUBSET-APPEND-GIVES-1))
 (3 3 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (3 3 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 )
(CLUSTER-SORT-BY-INSERTION
 (2023 29 (:DEFINITION ACL2-COUNT))
 (629 34 (:DEFINITION INTEGER-ABS))
 (486 167 (:REWRITE DEFAULT-+-2))
 (425 51 (:REWRITE |(+ y x)|))
 (323 17 (:REWRITE |(+ (if a b c) x)|))
 (217 167 (:REWRITE DEFAULT-+-1))
 (187 17 (:REWRITE NUMERATOR-NEGATIVE))
 (170 17 (:DEFINITION LENGTH))
 (167 167 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (167 167 (:REWRITE NORMALIZE-ADDENDS))
 (119 17 (:DEFINITION LEN))
 (102 34 (:REWRITE DEFAULT-UNARY-MINUS))
 (70 70 (:REWRITE DEFAULT-CAR))
 (68 68 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 2))
 (68 68 (:TYPE-PRESCRIPTION NUMERATOR-POSITIVE . 1))
 (68 68 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 2))
 (68 68 (:TYPE-PRESCRIPTION NUMERATOR-NEGATIVE . 1))
 (68 68 (:REWRITE DEFAULT-CDR))
 (56 56 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (56 56 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (55 55 (:REWRITE |(< (- x) (- y))|))
 (51 51 (:REWRITE |(< (- x) 0)|))
 (50 50 (:REWRITE FOLD-CONSTS-IN-+))
 (50 50 (:REWRITE |(+ c (+ d x))|))
 (44 38 (:REWRITE SIMPLIFY-SUMS-<))
 (44 38 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (44 38 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (42 38 (:REWRITE DEFAULT-<-2))
 (40 38 (:REWRITE DEFAULT-<-1))
 (34 34 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-<-0))
 (17 17 (:TYPE-PRESCRIPTION LEN))
 (17 17 (:REWRITE REDUCE-INTEGERP-+))
 (17 17 (:REWRITE INTEGERP==>NUMERATOR-=-X))
 (17 17 (:REWRITE INTEGERP==>DENOMINATOR-=-1))
 (17 17 (:REWRITE INTEGERP-MINUS-X))
 (17 17 (:REWRITE DEFAULT-REALPART))
 (17 17 (:REWRITE DEFAULT-NUMERATOR))
 (17 17 (:REWRITE DEFAULT-IMAGPART))
 (17 17 (:REWRITE DEFAULT-DENOMINATOR))
 (17 17 (:REWRITE DEFAULT-COERCE-2))
 (17 17 (:REWRITE DEFAULT-COERCE-1))
 (17 17 (:META META-INTEGERP-CORRECT))
 (12 12 (:LINEAR SUBTREEP-SMALLER))
 (12 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 4 (:REWRITE |(equal (+ d x) (+ c y))|))
 (12 4 (:REWRITE |(equal (+ c x) (+ d y))|))
 (8 4 (:REWRITE |(equal (+ c x) d)|))
 (6 2 (:REWRITE |(< (+ d x) (+ c y))|))
 (6 2 (:REWRITE |(< (+ c x) (+ d y))|))
 (4 4 (:REWRITE |(equal (- x) (- y))|))
 (4 2 (:REWRITE |(< (+ c x) d)|))
 )
(CLUSTER-SORT-BY-INSERTION-WHEN-NOT-CONSP)
(CLUSTER-SORT-BY-INSERTION-OF-CONSP
 (1076 12 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (956 4 (:DEFINITION HONS-ASSOC-EQUAL))
 (696 26 (:REWRITE PERM-IMPLIES-SUBSET))
 (550 14 (:REWRITE CONSP-SUBSET-MEMBER-FIRST-TAXON))
 (508 12 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (206 18 (:REWRITE SUBSET-SAME-MEMBERS))
 (206 14 (:REWRITE TASPI-T-SUBSET-MYTIPS-GIVES-MEMBER-GEN-FIRST))
 (162 2 (:REWRITE PERM-OF-CONSP))
 (152 2 (:REWRITE INTEGER-HALISTP-HALISTP))
 (150 27 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (148 4 (:DEFINITION INTEGER-HALISTP))
 (144 36 (:REWRITE PERM-WHEN-NOT-CONSP))
 (125 25 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (108 108 (:REWRITE CLUSTER-SORT-BY-INSERTION-WHEN-NOT-CONSP))
 (106 18 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (96 24 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (94 2 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (90 2 (:REWRITE GOOD-TAXON-INDEX-HALIST-OF-CONSP))
 (89 77 (:REWRITE DEFAULT-CDR))
 (89 71 (:REWRITE DEFAULT-CAR))
 (84 84 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (84 12 (:REWRITE TIP-P-GIVES-TASPIP-T))
 (75 75 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (72 72 (:TYPE-PRESCRIPTION PERM))
 (72 72 (:TYPE-PRESCRIPTION MYTIPS))
 (72 72 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (72 48 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (68 14 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (62 62 (:REWRITE CONSP-GIVES-CONSP-PAIR-KEY))
 (60 24 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (56 14 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (50 14 (:REWRITE SUBSET-STRIP-CARS-PAIR-GIVES-MEMBER-GEN-FIRST-TAXON))
 (48 12 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (36 36 (:TYPE-PRESCRIPTION TASPIP))
 (33 33 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (32 32 (:TYPE-PRESCRIPTION TIP-P))
 (32 4 (:DEFINITION HONS-EQUAL))
 (28 28 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (26 26 (:REWRITE SUBSET-TRANSITIVE))
 (26 26 (:REWRITE SUBSET-APPEND-GIVES-2))
 (26 26 (:REWRITE SUBSET-APPEND-GIVES-1))
 (26 10 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (24 12 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (20 12 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (18 18 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (16 16 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (16 16 (:REWRITE NOT-MEMBER-SUBSET))
 (16 4 (:REWRITE FIRST-TAXON-WHEN-NOT-CONSP))
 (14 14 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (14 14 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (12 12 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (10 10 (:REWRITE REDUCE-INTEGERP-+))
 (10 10 (:REWRITE INTEGERP-MINUS-X))
 (10 10 (:META META-INTEGERP-CORRECT))
 (10 2 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (8 4 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (8 4 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (8 4 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (8 2 (:REWRITE DEL-WHEN-NOT-CONSP))
 (4 4 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (4 4 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:REWRITE TASPIP-STRIP-CARS-PAIR))
 (2 2 (:REWRITE SUBSET-MYTIPS-GIVES-SUBSET-STRIP-CARS-PAIR))
 (2 2 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 )
(TASPIP-NIL-STRIP-CDRS-TASPIP-NIL-SORT
 (185 21 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (98 7 (:REWRITE INTEGER-HALISTP-HALISTP))
 (92 2 (:DEFINITION HONS-ASSOC-EQUAL))
 (77 16 (:REWRITE PERM-WHEN-NOT-CONSP))
 (77 7 (:DEFINITION INTEGER-HALISTP))
 (61 19 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (57 6 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (40 10 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (35 35 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (34 19 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (33 33 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (31 31 (:TYPE-PRESCRIPTION PERM))
 (31 1 (:REWRITE SUBSET-OF-CONSP))
 (30 30 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (28 7 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (25 21 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (23 20 (:REWRITE DEFAULT-CDR))
 (22 22 (:REWRITE DEFAULT-CAR))
 (21 6 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (19 1 (:REWRITE PERM-OF-CONSP))
 (18 18 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (14 14 (:REWRITE SUBSET-APPEND-GIVES-2))
 (14 14 (:REWRITE SUBSET-APPEND-GIVES-1))
 (14 14 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (12 12 (:REWRITE SUBSET-SAME-MEMBERS))
 (12 12 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (12 12 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (12 12 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (10 2 (:DEFINITION HONS-EQUAL))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (7 7 (:META META-INTEGERP-CORRECT))
 (6 6 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (4 4 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (4 1 (:REWRITE DEL-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 )
(CONSP-GIVES-CONSP-SORT
 (46 1 (:DEFINITION HONS-ASSOC-EQUAL))
 (30 3 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (28 2 (:REWRITE INTEGER-HALISTP-HALISTP))
 (22 2 (:DEFINITION INTEGER-HALISTP))
 (12 3 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (12 3 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (10 10 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (9 9 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (8 8 (:REWRITE DEFAULT-CAR))
 (8 2 (:REWRITE PERM-WHEN-NOT-CONSP))
 (8 2 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (7 7 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (6 6 (:REWRITE DEFAULT-CDR))
 (5 1 (:DEFINITION HONS-EQUAL))
 (4 4 (:TYPE-PRESCRIPTION PERM))
 (4 4 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (4 4 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (4 4 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (4 1 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (3 3 (:REWRITE SUBSET-SAME-MEMBERS))
 (3 3 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (2 2 (:META META-INTEGERP-CORRECT))
 (1 1 (:REWRITE SUBSET-APPEND-GIVES-2))
 (1 1 (:REWRITE SUBSET-APPEND-GIVES-1))
 (1 1 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE GREATER-ALL-GIVES-MEMBER-KEY))
 (1 1 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (1 1 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(SUBSET-MYTIPS-SORT
 (138 3 (:DEFINITION HONS-ASSOC-EQUAL))
 (111 33 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (84 9 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (84 6 (:REWRITE INTEGER-HALISTP-HALISTP))
 (78 16 (:REWRITE PERM-WHEN-NOT-CONSP))
 (73 1 (:REWRITE SUBSET-MYTIPS-GIVES-SUBSET-CDR))
 (66 6 (:DEFINITION INTEGER-HALISTP))
 (52 52 (:TYPE-PRESCRIPTION MYTIPS))
 (44 11 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (33 33 (:TYPE-PRESCRIPTION STRIP-CDRS-GEN))
 (33 33 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (32 8 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (30 9 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (29 13 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (28 28 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (27 27 (:TYPE-PRESCRIPTION PERM))
 (26 26 (:REWRITE DEFAULT-CAR))
 (25 22 (:REWRITE DEFAULT-CDR))
 (24 24 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (24 6 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (17 17 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (15 3 (:DEFINITION HONS-EQUAL))
 (14 14 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (13 13 (:REWRITE SUBSET-APPEND-GIVES-2))
 (13 13 (:REWRITE SUBSET-APPEND-GIVES-1))
 (13 13 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (12 12 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (11 11 (:REWRITE SUBSET-SAME-MEMBERS))
 (11 11 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (10 10 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (10 2 (:DEFINITION BINARY-APPEND))
 (9 9 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (9 3 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (6 6 (:META META-INTEGERP-CORRECT))
 (6 3 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (5 5 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (4 1 (:REWRITE ATOM-CDR-ASSOC-GOOD-TAXON-LIST))
 (3 3 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (3 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:TYPE-PRESCRIPTION GOOD-INDEX-TAXON-HALIST))
 (2 2 (:REWRITE SUBSET-THROUGH-DEL-PAIR))
 (2 2 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (2 2 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 (1 1 (:REWRITE GREATER-ALL-GIVES-MEMBER-KEY))
 (1 1 (:REWRITE GOOD-INDEX-TAXON-HALIST-WHEN-NOT-CONSP))
 )
(SUBSET-MYTIPS-CLUSTER-SORT-BY-INSERTION
 (125 30 (:REWRITE PERM-WHEN-NOT-CONSP))
 (58 58 (:TYPE-PRESCRIPTION PERM))
 (53 13 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (42 42 (:TYPE-PRESCRIPTION PAIR-KEY-WITH-VALUE))
 (35 7 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (35 7 (:DEFINITION BINARY-APPEND))
 (26 26 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (25 25 (:REWRITE SUBSET-APPEND-GIVES-2))
 (25 25 (:REWRITE SUBSET-APPEND-GIVES-1))
 (24 24 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (24 8 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (24 8 (:REWRITE SORT-THE-ALIST-BY-INSERTION-OF-CONSP))
 (21 21 (:TYPE-PRESCRIPTION STRIP-CDRS-GEN))
 (20 8 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (14 14 (:REWRITE CONSP-GIVES-CONSP-PAIR-KEY))
 (13 13 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (12 1 (:REWRITE PERM-OF-CONSP))
 (11 11 (:REWRITE DEFAULT-CDR))
 (11 11 (:REWRITE DEFAULT-CAR))
 (9 3 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (9 3 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (8 8 (:TYPE-PRESCRIPTION GREATER-ALL))
 (5 5 (:REWRITE SUBSET-SAME-MEMBERS))
 (5 5 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (5 5 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (4 4 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (4 4 (:REWRITE NOT-MEMBER-SUBSET))
 (4 4 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (4 1 (:REWRITE DEL-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION BINARY-APPEND))
 )
(TASPIP-CLUSTER-SORT-BY-INSERTION
 (1281 271 (:DEFINITION TRUE-LISTP))
 (1046 1046 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (542 124 (:REWRITE PERM-WHEN-NOT-CONSP))
 (414 393 (:REWRITE DEFAULT-CDR))
 (234 234 (:TYPE-PRESCRIPTION PERM))
 (233 233 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (213 3 (:DEFINITION HONS-ASSOC-EQUAL))
 (185 12 (:REWRITE PERM-OF-CONSP))
 (127 9 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (122 98 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (116 116 (:REWRITE SUBSET-APPEND-GIVES-2))
 (106 106 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (105 96 (:REWRITE DEFAULT-CAR))
 (91 4 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (84 84 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (82 7 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (81 81 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (66 33 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (60 18 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (57 9 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (48 12 (:REWRITE DEL-WHEN-NOT-CONSP))
 (47 4 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (44 12 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (38 2 (:REWRITE SUBSET-SUBSET-GIVES-SUBSET-APPEND))
 (36 12 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (31 31 (:REWRITE SUBSET-SAME-MEMBERS))
 (31 31 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (24 24 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (18 18 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (18 18 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (18 18 (:REWRITE NOT-MEMBER-SUBSET))
 (15 3 (:DEFINITION HONS-EQUAL))
 (12 12 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (12 12 (:REWRITE REDUCE-INTEGERP-+))
 (12 12 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (12 12 (:REWRITE INTEGERP-MINUS-X))
 (12 12 (:META META-INTEGERP-CORRECT))
 (12 3 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (11 5 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (10 4 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (9 3 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 (6 6 (:TYPE-PRESCRIPTION ALISTP-GEN))
 (4 4 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (3 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (3 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (3 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 )
(MEMBER-GEN-ALISTP-GEN-GIVES-CONSP
 (430 45 (:REWRITE SUBSET-SAME-MEMBERS))
 (418 20 (:REWRITE INTEGER-HALISTP-HALISTP))
 (373 27 (:DEFINITION INTEGER-HALISTP))
 (217 46 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (192 48 (:REWRITE PERM-WHEN-NOT-CONSP))
 (152 38 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (119 119 (:REWRITE DEFAULT-CAR))
 (113 113 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (105 105 (:REWRITE DEFAULT-CDR))
 (104 26 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (99 22 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (96 96 (:TYPE-PRESCRIPTION PERM))
 (84 21 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (82 82 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (82 82 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (80 20 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (77 11 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (45 45 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (41 41 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (40 40 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (37 37 (:REWRITE REDUCE-INTEGERP-+))
 (37 37 (:REWRITE INTEGERP-MINUS-X))
 (37 37 (:META META-INTEGERP-CORRECT))
 (30 2 (:REWRITE PERM-OF-CONSP))
 (28 28 (:REWRITE SUBSET-TRANSITIVE))
 (28 28 (:REWRITE SUBSET-APPEND-GIVES-2))
 (28 28 (:REWRITE SUBSET-APPEND-GIVES-1))
 (24 2 (:REWRITE SUBSET-OF-CONSP))
 (22 22 (:TYPE-PRESCRIPTION TIP-P))
 (20 20 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (12 12 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 12 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 12 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 12 (:REWRITE |(equal (- x) (- y))|))
 (8 2 (:REWRITE DEL-WHEN-NOT-CONSP))
 )
(ALISTP-GEN-SORT
 (386 16 (:REWRITE INTEGER-HALISTP-HALISTP))
 (339 17 (:DEFINITION INTEGER-HALISTP))
 (149 16 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (92 2 (:DEFINITION HONS-ASSOC-EQUAL))
 (91 91 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (65 25 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (61 13 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (60 1 (:REWRITE GOOD-TAXON-INDEX-HALIST-OF-CONSP))
 (59 40 (:REWRITE DEFAULT-CDR))
 (57 6 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (44 42 (:REWRITE DEFAULT-CAR))
 (38 38 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (38 38 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (32 8 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (31 15 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (22 22 (:REWRITE REDUCE-INTEGERP-+))
 (22 22 (:REWRITE INTEGERP-MINUS-X))
 (22 22 (:META META-INTEGERP-CORRECT))
 (22 5 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (21 6 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (20 5 (:REWRITE PERM-WHEN-NOT-CONSP))
 (18 9 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (16 4 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (15 3 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (14 14 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (12 3 (:REWRITE EQUAL-CAR-ASSOC-KEY))
 (11 11 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (10 10 (:TYPE-PRESCRIPTION PERM))
 (10 10 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (10 2 (:DEFINITION HONS-EQUAL))
 (8 8 (:REWRITE SUBSET-SAME-MEMBERS))
 (8 8 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (6 6 (:TYPE-PRESCRIPTION TIP-P))
 (5 5 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (4 4 (:REWRITE SUBSET-THROUGH-DEL-PAIR))
 (4 4 (:REWRITE SUBSET-APPEND-GIVES-2))
 (4 4 (:REWRITE SUBSET-APPEND-GIVES-1))
 (4 4 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (4 4 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 (2 2 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (2 2 (:REWRITE CAR-CONS))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE CDR-CONS))
 )
(CLUSTER-SORT-BY-INSERTION
 (283 1 (:REWRITE INTEGER-HALISTP-HALISTP))
 (281 2 (:DEFINITION INTEGER-HALISTP))
 (244 1 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (242 1 (:REWRITE GOOD-TAXON-INDEX-HALIST-OF-CONSP))
 (187 38 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (186 33 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (169 40 (:REWRITE PERM-WHEN-NOT-CONSP))
 (163 43 (:REWRITE DEFAULT-CDR))
 (150 2 (:DEFINITION HONS-ASSOC-EQUAL))
 (119 23 (:DEFINITION TRUE-LISTP))
 (103 103 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (101 3 (:REWRITE EQUAL-CAR-ASSOC-KEY))
 (92 6 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (80 80 (:TYPE-PRESCRIPTION PERM))
 (80 2 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (79 20 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (77 17 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (73 57 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (70 46 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (68 68 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (58 2 (:REWRITE SUBSET-THROUGH-DEL-PAIR))
 (45 45 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (38 38 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (37 6 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (36 36 (:REWRITE CLUSTER-SORT-BY-INSERTION-WHEN-NOT-CONSP))
 (33 33 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (33 23 (:REWRITE DEFAULT-CAR))
 (27 9 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (21 21 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (20 17 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (20 5 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (18 18 (:REWRITE SUBSET-APPEND-GIVES-2))
 (18 6 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (17 17 (:REWRITE SUBSET-MYTIPS-GIVES-SUBSET-STRIP-CARS-PAIR))
 (16 16 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (16 4 (:REWRITE TIP-P-GIVES-TASPIP-T))
 (14 14 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (10 10 (:TYPE-PRESCRIPTION TIP-P))
 (10 2 (:DEFINITION HONS-EQUAL))
 (10 2 (:DEFINITION BINARY-APPEND))
 (9 9 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (7 7 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (7 3 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (6 6 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (6 2 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (5 5 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (5 5 (:REWRITE SUBSET-SAME-MEMBERS))
 (5 5 (:REWRITE REDUCE-INTEGERP-+))
 (5 5 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (5 5 (:REWRITE INTEGERP-MINUS-X))
 (5 5 (:META META-INTEGERP-CORRECT))
 (4 4 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (4 1 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (3 3 (:REWRITE TASPIP-STRIP-CARS-PAIR))
 (2 2 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (2 2 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (2 2 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (2 2 (:REWRITE CAR-CONS))
 (2 2 (:REWRITE |(equal (- x) (- y))|))
 (1 1 (:REWRITE SUBSET-SUBSET-GIVES-SUBSET-APPEND))
 (1 1 (:REWRITE CDR-CONS))
 )
(ORDER-BY-INSERTION-HELP)
(MAX-LIST-HELPER)
(MAX-LIST
 (5 5 (:TYPE-PRESCRIPTION MAX-LIST-HELPER))
 )
(ORDER-BY-INSERTION)
(ORDER-BY-INSERTION-ONE-LEVEL
 (28 2 (:DEFINITION MAX-LIST-HELPER))
 (15 2 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE DEFAULT-+-2))
 (10 10 (:REWRITE DEFAULT-+-1))
 (10 2 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (9 1 (:REWRITE PERM-IMPLIES-SUBSET))
 (8 8 (:REWRITE DEFAULT-CAR))
 (8 1 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (7 7 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (7 7 (:REWRITE DEFAULT-CDR))
 (5 5 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (5 1 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (5 1 (:REWRITE SORT-THE-ALIST-BY-INSERTION-OF-CONSP))
 (5 1 (:DEFINITION TRUE-LISTP))
 (4 4 (:REWRITE CONSP-GIVES-CONSP-PAIR-KEY))
 (4 1 (:REWRITE TIP-P-GIVES-TASPIP-T))
 (4 1 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (4 1 (:REWRITE PERM-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION MAX-LIST-HELPER))
 (3 3 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (3 3 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (2 2 (:TYPE-PRESCRIPTION TIP-P))
 (2 2 (:TYPE-PRESCRIPTION PERM))
 (2 2 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (2 2 (:REWRITE SIMPLIFY-SUMS-<))
 (2 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (2 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 2 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 (1 1 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (1 1 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (1 1 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (1 1 (:REWRITE SUBSET-TRANSITIVE))
 (1 1 (:REWRITE SUBSET-APPEND-GIVES-2))
 (1 1 (:REWRITE SUBSET-APPEND-GIVES-1))
 (1 1 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (1 1 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (1 1 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 )
(ORDERED-NIL-STRIP-CDRS-ORDERED-NIL-STRIP-SORT
 (98 7 (:REWRITE INTEGER-HALISTP-HALISTP))
 (77 7 (:DEFINITION INTEGER-HALISTP))
 (54 29 (:REWRITE DEFAULT-CDR))
 (49 30 (:REWRITE DEFAULT-CAR))
 (46 1 (:DEFINITION HONS-ASSOC-EQUAL))
 (35 35 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (35 23 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (32 8 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (31 7 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (30 3 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (29 29 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (28 7 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (24 6 (:REWRITE PERM-WHEN-NOT-CONSP))
 (21 21 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (20 5 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (15 15 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (14 14 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION PERM))
 (12 3 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (11 11 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (10 10 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (8 8 (:REWRITE SUBSET-SAME-MEMBERS))
 (8 8 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (7 7 (:REWRITE REDUCE-INTEGERP-+))
 (7 7 (:REWRITE INTEGERP-MINUS-X))
 (7 7 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (7 7 (:META META-INTEGERP-CORRECT))
 (6 6 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (5 5 (:REWRITE SUBSET-APPEND-GIVES-2))
 (5 5 (:REWRITE SUBSET-APPEND-GIVES-1))
 (5 1 (:DEFINITION HONS-EQUAL))
 (4 1 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (2 2 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (2 2 (:REWRITE SUBSET-THROUGH-DEL-PAIR))
 (2 2 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (2 2 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 (1 1 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1 1 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1 1 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (1 1 (:REWRITE |(equal (- x) (- y))|))
 )
(ORDERED-NIL-THROUGH-SORT
 (13 2 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (9 9 (:TYPE-PRESCRIPTION PAIR-KEY-WITH-VALUE))
 (5 1 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (5 1 (:REWRITE SORT-THE-ALIST-BY-INSERTION-OF-CONSP))
 (4 1 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (4 1 (:DEFINITION ORDEREDP))
 (3 3 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (3 3 (:REWRITE CONSP-GIVES-CONSP-PAIR-KEY))
 (2 2 (:TYPE-PRESCRIPTION GREATER-ALL))
 (1 1 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (1 1 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-CAR))
 )
(CLUSTER-T-DOESNT-CHANGE-ORDERED-NIL
 (34 6 (:REWRITE TASPIP-CLUSTER-SORT-BY-INSERTION))
 (18 2 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (16 2 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION TASPIP))
 (12 12 (:TYPE-PRESCRIPTION PAIR-KEY-WITH-VALUE))
 (12 2 (:REWRITE SORT-THE-ALIST-BY-INSERTION-OF-CONSP))
 (10 2 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (8 4 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (8 2 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (6 6 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (6 4 (:REWRITE CONSP-GIVES-CONSP-PAIR-KEY))
 (4 4 (:TYPE-PRESCRIPTION GREATER-ALL))
 (4 4 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (4 4 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (4 4 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (3 3 (:REWRITE DEFAULT-CDR))
 (3 3 (:REWRITE DEFAULT-CAR))
 (2 2 (:TYPE-PRESCRIPTION STRIP-CDRS-GEN))
 (2 2 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 )
(ASSOC-MIN-KEY-WHEN-NOT-INPUT
 (4608 2304 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (2976 66 (:DEFINITION HONS-ASSOC-EQUAL))
 (2478 198 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (2304 2304 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (804 204 (:REWRITE DEFAULT-CDR))
 (750 198 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (744 192 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (651 646 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (572 572 (:TYPE-PRESCRIPTION MEMBER-GEN))
 (552 552 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (420 60 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (368 368 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (328 45 (:REWRITE SIMPLIFY-SUMS-<))
 (328 45 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (328 45 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (328 45 (:REWRITE DEFAULT-<-1))
 (286 286 (:REWRITE SUBSET-SAME-MEMBERS))
 (286 286 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (286 286 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (270 66 (:DEFINITION HONS-EQUAL))
 (252 252 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (243 45 (:REWRITE DEFAULT-<-2))
 (238 34 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (192 192 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (192 192 (:REWRITE NOT-MEMBER-SUBSET))
 (184 184 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (73 73 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (73 73 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (73 73 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (73 73 (:REWRITE |(equal (- x) (- y))|))
 (45 45 (:REWRITE |(< (- x) (- y))|))
 (40 40 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (34 34 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 )
(IF-KEY-CUR-MIN-PAIR
 (4780 2390 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (3564 78 (:DEFINITION HONS-ASSOC-EQUAL))
 (2721 234 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (2390 2390 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (826 236 (:REWRITE DEFAULT-CDR))
 (786 234 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (767 215 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (612 612 (:TYPE-PRESCRIPTION MEMBER-GEN))
 (552 552 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (413 59 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (370 367 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (368 368 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (366 78 (:DEFINITION HONS-EQUAL))
 (306 306 (:REWRITE SUBSET-SAME-MEMBERS))
 (306 306 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (306 306 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (304 28 (:REWRITE SIMPLIFY-SUMS-<))
 (304 28 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (304 28 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (304 28 (:REWRITE DEFAULT-<-1))
 (280 28 (:REWRITE DEFAULT-<-2))
 (274 274 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (224 32 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (215 215 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (215 215 (:REWRITE NOT-MEMBER-SUBSET))
 (184 184 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (96 17 (:REWRITE ASSOC-MIN-KEY-WHEN-NOT-INPUT))
 (88 88 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (88 88 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (88 88 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (88 88 (:REWRITE |(equal (- x) (- y))|))
 (32 32 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (28 28 (:REWRITE |(< (- x) (- y))|))
 (24 24 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 )
(EXISTS-KEY-<-THEN-LESS
 (11634 5817 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (6576 108 (:DEFINITION HONS-ASSOC-EQUAL))
 (6417 324 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (5981 5981 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (2303 559 (:REWRITE SUBSET-SAME-MEMBERS))
 (1565 555 (:REWRITE DEFAULT-CDR))
 (1357 561 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (1321 343 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (1224 324 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (1129 1120 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (1104 90 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (846 79 (:REWRITE SIMPLIFY-SUMS-<))
 (846 79 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (846 79 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (846 79 (:REWRITE DEFAULT-<-1))
 (835 835 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (830 28 (:REWRITE INTEGER-HALISTP-HALISTP))
 (797 224 (:REWRITE PERM-WHEN-NOT-CONSP))
 (758 40 (:DEFINITION INTEGER-HALISTP))
 (707 101 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (656 656 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (591 591 (:REWRITE DEFAULT-CAR))
 (559 559 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (540 108 (:DEFINITION HONS-EQUAL))
 (448 448 (:TYPE-PRESCRIPTION PERM))
 (425 122 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (350 350 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (328 328 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (234 52 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (185 79 (:REWRITE DEFAULT-<-2))
 (182 26 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (142 8 (:REWRITE SUBSET-OF-CONSP))
 (135 135 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (130 130 (:REWRITE SUBSET-TRANSITIVE))
 (130 130 (:REWRITE SUBSET-APPEND-GIVES-2))
 (130 130 (:REWRITE SUBSET-APPEND-GIVES-1))
 (120 8 (:REWRITE PERM-OF-CONSP))
 (118 118 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (118 118 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (118 118 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (118 118 (:REWRITE |(equal (- x) (- y))|))
 (112 28 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (79 79 (:REWRITE |(< (- x) (- y))|))
 (78 78 (:REWRITE REDUCE-INTEGERP-+))
 (78 78 (:REWRITE INTEGERP-MINUS-X))
 (78 78 (:META META-INTEGERP-CORRECT))
 (69 69 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (60 60 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (52 52 (:TYPE-PRESCRIPTION TIP-P))
 (35 35 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (32 8 (:REWRITE DEL-WHEN-NOT-CONSP))
 (28 28 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (18 3 (:REWRITE ASSOC-MIN-KEY-WHEN-NOT-INPUT))
 )
(GREATER-ALL-MIN-KEY-<
 (8548 142 (:DEFINITION HONS-ASSOC-EQUAL))
 (8248 4124 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (7058 426 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (5574 426 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (4266 4266 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (2125 469 (:REWRITE SUBSET-SAME-MEMBERS))
 (1458 1458 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (1400 356 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (1365 1355 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (1115 116 (:REWRITE PERM-IMPLIES-SUBSET))
 (893 621 (:REWRITE DEFAULT-CDR))
 (817 204 (:REWRITE PERM-WHEN-NOT-CONSP))
 (779 26 (:REWRITE INTEGER-HALISTP-HALISTP))
 (732 732 (:REWRITE DEFAULT-CAR))
 (718 42 (:DEFINITION INTEGER-HALISTP))
 (710 142 (:DEFINITION HONS-EQUAL))
 (572 50 (:REWRITE SIMPLIFY-SUMS-<))
 (572 50 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (572 50 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (572 50 (:REWRITE DEFAULT-<-1))
 (544 136 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (543 543 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (469 469 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (407 407 (:TYPE-PRESCRIPTION PERM))
 (358 358 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (356 356 (:REWRITE NOT-MEMBER-SUBSET))
 (283 283 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (240 50 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (198 44 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (180 50 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (154 22 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (143 143 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (143 143 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (143 143 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (143 143 (:REWRITE |(equal (- x) (- y))|))
 (116 116 (:REWRITE SUBSET-TRANSITIVE))
 (116 116 (:REWRITE SUBSET-APPEND-GIVES-2))
 (116 116 (:REWRITE SUBSET-APPEND-GIVES-1))
 (103 50 (:REWRITE DEFAULT-<-2))
 (75 75 (:REWRITE REDUCE-INTEGERP-+))
 (75 75 (:REWRITE INTEGERP-MINUS-X))
 (75 75 (:META META-INTEGERP-CORRECT))
 (74 74 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (50 50 (:REWRITE |(< (- x) (- y))|))
 (30 30 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (28 28 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (26 26 (:REWRITE EXISTS-KEY-<-THEN-LESS))
 (25 25 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (6 1 (:REWRITE ASSOC-MIN-KEY-WHEN-NOT-INPUT))
 )
(VALID-PAIRING-THROUGH-SORT
 (84 6 (:REWRITE INTEGER-HALISTP-HALISTP))
 (66 6 (:DEFINITION INTEGER-HALISTP))
 (53 51 (:REWRITE DEFAULT-CAR))
 (46 1 (:DEFINITION HONS-ASSOC-EQUAL))
 (45 38 (:REWRITE DEFAULT-CDR))
 (44 11 (:REWRITE VALID-PAIRING-CDR))
 (30 30 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (30 3 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (28 7 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (25 25 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (24 6 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (22 22 (:TYPE-PRESCRIPTION FIRST-TAXON))
 (20 5 (:REWRITE PERM-WHEN-NOT-CONSP))
 (18 3 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (16 4 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (13 13 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (12 12 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 12 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 12 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 12 (:REWRITE |(equal (- x) (- y))|))
 (12 3 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (11 11 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (11 11 (:REWRITE FIRST-TAXON-WHEN-NOT-CONSP))
 (10 10 (:TYPE-PRESCRIPTION PERM))
 (10 10 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (9 9 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (7 7 (:REWRITE SUBSET-SAME-MEMBERS))
 (7 7 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (6 6 (:META META-INTEGERP-CORRECT))
 (5 5 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (5 1 (:DEFINITION HONS-EQUAL))
 (4 4 (:REWRITE SUBSET-APPEND-GIVES-2))
 (4 4 (:REWRITE SUBSET-APPEND-GIVES-1))
 (4 1 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (2 2 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (2 2 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (1 1 (:REWRITE SUBSET-THROUGH-DEL-PAIR))
 (1 1 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (1 1 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 )
(GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS
 (12600 6300 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (10736 185 (:DEFINITION HONS-ASSOC-EQUAL))
 (10132 555 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (6508 6508 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (3436 854 (:REWRITE SUBSET-SAME-MEMBERS))
 (2645 875 (:REWRITE DEFAULT-CDR))
 (2121 585 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (2074 856 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (1977 555 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (1313 1313 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (1239 177 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (1189 1181 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (1183 67 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (1133 323 (:REWRITE PERM-WHEN-NOT-CONSP))
 (1087 34 (:REWRITE INTEGER-HALISTP-HALISTP))
 (1016 1016 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (1004 53 (:DEFINITION INTEGER-HALISTP))
 (953 953 (:REWRITE DEFAULT-CAR))
 (925 185 (:DEFINITION HONS-EQUAL))
 (854 854 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (646 646 (:TYPE-PRESCRIPTION PERM))
 (624 56 (:REWRITE SIMPLIFY-SUMS-<))
 (624 56 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (624 56 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (624 56 (:REWRITE DEFAULT-<-1))
 (592 592 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (579 171 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (572 56 (:REWRITE DEFAULT-<-2))
 (508 508 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (288 64 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (234 234 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (234 234 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (234 234 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (234 234 (:REWRITE |(equal (- x) (- y))|))
 (224 32 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (179 179 (:REWRITE SUBSET-TRANSITIVE))
 (179 179 (:REWRITE SUBSET-APPEND-GIVES-2))
 (179 179 (:REWRITE SUBSET-APPEND-GIVES-1))
 (142 8 (:REWRITE SUBSET-OF-CONSP))
 (136 136 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (136 34 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (120 8 (:REWRITE PERM-OF-CONSP))
 (105 105 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (104 104 (:REWRITE REDUCE-INTEGERP-+))
 (104 104 (:REWRITE INTEGERP-MINUS-X))
 (104 104 (:META META-INTEGERP-CORRECT))
 (67 67 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (64 64 (:TYPE-PRESCRIPTION TIP-P))
 (56 56 (:REWRITE |(< (- x) (- y))|))
 (49 49 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (34 34 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (32 8 (:REWRITE DEL-WHEN-NOT-CONSP))
 )
(CHECK-LESS
 (84 42 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (42 42 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (21 21 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 )
(GET-MIN-KEY2
 (1528 18 (:DEFINITION HONS-ASSOC-EQUAL))
 (1256 48 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (970 485 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (844 48 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (596 596 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (495 23 (:REWRITE INTEGER-HALISTP-HALISTP))
 (448 72 (:REWRITE SUBSET-SAME-MEMBERS))
 (433 27 (:DEFINITION INTEGER-HALISTP))
 (431 45 (:REWRITE PERM-IMPLIES-SUBSET))
 (254 65 (:REWRITE PERM-WHEN-NOT-CONSP))
 (252 8 (:REWRITE ASSOC-HQUAL-FROM-MEMBER-GEN-STRIP-CARS))
 (246 244 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (244 56 (:REWRITE NOT-MEMBER-SUBSET))
 (242 72 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (218 56 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (180 45 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (178 146 (:REWRITE DEFAULT-CDR))
 (147 147 (:REWRITE DEFAULT-CAR))
 (135 30 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (134 134 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (130 130 (:TYPE-PRESCRIPTION PERM))
 (105 15 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (98 98 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (90 18 (:DEFINITION HONS-EQUAL))
 (80 23 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (72 72 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (72 72 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (64 16 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (56 56 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (45 45 (:REWRITE SUBSET-TRANSITIVE))
 (45 45 (:REWRITE SUBSET-APPEND-GIVES-2))
 (45 45 (:REWRITE SUBSET-APPEND-GIVES-1))
 (43 43 (:REWRITE REDUCE-INTEGERP-+))
 (43 43 (:REWRITE INTEGERP-MINUS-X))
 (43 43 (:META META-INTEGERP-CORRECT))
 (28 2 (:REWRITE SIMPLIFY-SUMS-<))
 (28 2 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (28 2 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (28 2 (:REWRITE DEFAULT-<-1))
 (24 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (20 2 (:REWRITE DEFAULT-<-2))
 (19 19 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (18 18 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (18 18 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (18 18 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (18 18 (:REWRITE |(equal (- x) (- y))|))
 (18 6 (:REWRITE ASSOC-CAR-FROM-SUBSET))
 (15 15 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (14 2 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (8 8 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (6 6 (:REWRITE MEMBER-GIVES-ASSOC-HQUAL))
 (2 2 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (2 2 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (2 2 (:REWRITE |(< (- x) (- y))|))
 )
(PAIR-KEY-CUR-MIN-SAME-AS-GET-MIN2
 (4112 90 (:DEFINITION HONS-ASSOC-EQUAL))
 (3381 270 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (2470 1235 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (1235 1235 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (1202 322 (:REWRITE DEFAULT-CDR))
 (969 270 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (967 268 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (782 782 (:TYPE-PRESCRIPTION MEMBER-GEN))
 (699 699 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (625 623 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (616 88 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (466 466 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (422 90 (:DEFINITION HONS-EQUAL))
 (410 31 (:REWRITE SIMPLIFY-SUMS-<))
 (410 31 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (410 31 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (410 31 (:REWRITE DEFAULT-<-1))
 (391 391 (:REWRITE SUBSET-SAME-MEMBERS))
 (391 391 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (391 391 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (356 356 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (326 31 (:REWRITE DEFAULT-<-2))
 (268 268 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (268 268 (:REWRITE NOT-MEMBER-SUBSET))
 (245 35 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (233 233 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (104 104 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (102 102 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (102 102 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (102 102 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (102 102 (:REWRITE |(equal (- x) (- y))|))
 (35 35 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (35 35 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (31 31 (:REWRITE |(< (- x) (- y))|))
 )
(GET-MIN-KEY=KEY-MIN-KEY2-GEN
 (552 12 (:DEFINITION HONS-ASSOC-EQUAL))
 (378 36 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (358 36 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (126 63 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (114 30 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (90 90 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (74 74 (:REWRITE DEFAULT-CAR))
 (70 70 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (65 45 (:REWRITE DEFAULT-CDR))
 (63 63 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (60 12 (:DEFINITION HONS-EQUAL))
 (42 3 (:REWRITE SIMPLIFY-SUMS-<))
 (42 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (42 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (42 3 (:REWRITE DEFAULT-<-2))
 (42 3 (:REWRITE DEFAULT-<-1))
 (41 41 (:REWRITE SUBSET-SAME-MEMBERS))
 (41 41 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (41 41 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (40 40 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (40 10 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (40 1 (:REWRITE INTEGER-HALISTP-HALISTP))
 (38 2 (:DEFINITION INTEGER-HALISTP))
 (30 30 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (30 30 (:REWRITE NOT-MEMBER-SUBSET))
 (26 26 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (21 3 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (21 3 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (15 15 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (12 12 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (12 12 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (12 12 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (12 12 (:REWRITE |(equal (- x) (- y))|))
 (9 2 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (9 1 (:REWRITE PERM-IMPLIES-SUBSET))
 (7 1 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (5 5 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (4 4 (:REWRITE REDUCE-INTEGERP-+))
 (4 4 (:REWRITE INTEGERP-MINUS-X))
 (4 4 (:META META-INTEGERP-CORRECT))
 (4 1 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (4 1 (:REWRITE PERM-WHEN-NOT-CONSP))
 (4 1 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 (2 2 (:TYPE-PRESCRIPTION TIP-P))
 (2 2 (:TYPE-PRESCRIPTION PERM))
 (1 1 (:REWRITE SUBSET-TRANSITIVE))
 (1 1 (:REWRITE SUBSET-APPEND-GIVES-2))
 (1 1 (:REWRITE SUBSET-APPEND-GIVES-1))
 (1 1 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (1 1 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (1 1 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 )
(NOT-EQUAL-GET-MIN2
 (11489 444 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (10902 148 (:DEFINITION HONS-ASSOC-EQUAL))
 (10486 5243 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (5395 5395 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (4490 756 (:REWRITE SUBSET-SAME-MEMBERS))
 (2469 756 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (2444 255 (:REWRITE PERM-IMPLIES-SUBSET))
 (2362 892 (:REWRITE DEFAULT-CDR))
 (2010 2010 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (1800 455 (:REWRITE PERM-WHEN-NOT-CONSP))
 (1650 468 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (1551 444 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (1510 1505 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (1029 147 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (972 468 (:REWRITE NOT-MEMBER-SUBSET))
 (909 909 (:TYPE-PRESCRIPTION PERM))
 (864 864 (:REWRITE DEFAULT-CAR))
 (838 24 (:REWRITE INTEGER-HALISTP-HALISTP))
 (785 42 (:DEFINITION INTEGER-HALISTP))
 (756 756 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (740 148 (:DEFINITION HONS-EQUAL))
 (662 53 (:REWRITE SIMPLIFY-SUMS-<))
 (662 53 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (662 53 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (662 53 (:REWRITE DEFAULT-<-1))
 (575 575 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (558 53 (:REWRITE DEFAULT-<-2))
 (518 74 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (476 74 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (468 468 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (255 255 (:REWRITE SUBSET-TRANSITIVE))
 (255 255 (:REWRITE SUBSET-APPEND-GIVES-2))
 (255 255 (:REWRITE SUBSET-APPEND-GIVES-1))
 (207 46 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (170 170 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (170 170 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (170 170 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (170 170 (:REWRITE |(equal (- x) (- y))|))
 (161 23 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (139 139 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (82 82 (:REWRITE REDUCE-INTEGERP-+))
 (82 82 (:REWRITE INTEGERP-MINUS-X))
 (82 82 (:META META-INTEGERP-CORRECT))
 (53 53 (:REWRITE |(< (- x) (- y))|))
 (46 46 (:TYPE-PRESCRIPTION TIP-P))
 (28 28 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (23 23 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 )
(GET-MIN2-<
 (7958 173 (:DEFINITION HONS-ASSOC-EQUAL))
 (7450 3725 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (5707 519 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (5535 519 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (3844 3844 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (1584 429 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (1287 1287 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (994 990 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (882 550 (:REWRITE DEFAULT-CDR))
 (865 173 (:DEFINITION HONS-EQUAL))
 (854 854 (:REWRITE DEFAULT-CAR))
 (664 166 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (664 19 (:REWRITE INTEGER-HALISTP-HALISTP))
 (622 33 (:DEFINITION INTEGER-HALISTP))
 (601 601 (:REWRITE SUBSET-SAME-MEMBERS))
 (601 601 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (601 601 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (464 38 (:REWRITE SIMPLIFY-SUMS-<))
 (464 38 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (464 38 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (464 38 (:REWRITE DEFAULT-<-1))
 (429 429 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (429 429 (:REWRITE NOT-MEMBER-SUBSET))
 (388 38 (:REWRITE DEFAULT-<-2))
 (315 45 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (309 45 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (204 23 (:REWRITE PERM-IMPLIES-SUBSET))
 (173 173 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (173 173 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (173 173 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (173 173 (:REWRITE |(equal (- x) (- y))|))
 (171 38 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (133 19 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (93 23 (:REWRITE PERM-WHEN-NOT-CONSP))
 (91 91 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (86 86 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (65 65 (:REWRITE REDUCE-INTEGERP-+))
 (65 65 (:REWRITE INTEGERP-MINUS-X))
 (65 65 (:META META-INTEGERP-CORRECT))
 (45 45 (:TYPE-PRESCRIPTION PERM))
 (38 38 (:TYPE-PRESCRIPTION TIP-P))
 (38 38 (:REWRITE |(< (- x) (- y))|))
 (23 23 (:REWRITE SUBSET-TRANSITIVE))
 (23 23 (:REWRITE SUBSET-APPEND-GIVES-2))
 (23 23 (:REWRITE SUBSET-APPEND-GIVES-1))
 (23 23 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (18 18 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 )
(GET-MIN-GIVES-CHECK-LESS-STRIP-CARS
 (17896 372 (:DEFINITION HONS-ASSOC-EQUAL))
 (13040 1116 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (12963 1116 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (12236 6118 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (6384 6384 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (3449 932 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (3061 3045 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (2907 2907 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (2010 1266 (:REWRITE DEFAULT-CDR))
 (2004 1298 (:REWRITE SUBSET-SAME-MEMBERS))
 (1914 1914 (:REWRITE DEFAULT-CAR))
 (1860 372 (:DEFINITION HONS-EQUAL))
 (1638 1298 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (1488 372 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (1465 42 (:REWRITE INTEGER-HALISTP-HALISTP))
 (1370 72 (:DEFINITION INTEGER-HALISTP))
 (1298 1298 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (1184 86 (:REWRITE SIMPLIFY-SUMS-<))
 (1184 86 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1184 86 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1184 86 (:REWRITE DEFAULT-<-1))
 (932 932 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (932 932 (:REWRITE NOT-MEMBER-SUBSET))
 (884 86 (:REWRITE DEFAULT-<-2))
 (724 92 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (632 92 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (493 126 (:REWRITE PERM-WHEN-NOT-CONSP))
 (378 84 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (372 372 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (372 372 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (372 372 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (372 372 (:REWRITE |(equal (- x) (- y))|))
 (330 330 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (294 42 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (264 264 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (251 251 (:TYPE-PRESCRIPTION PERM))
 (219 219 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (143 143 (:REWRITE REDUCE-INTEGERP-+))
 (143 143 (:REWRITE INTEGERP-MINUS-X))
 (143 143 (:META META-INTEGERP-CORRECT))
 (86 86 (:REWRITE SUBSET-APPEND-GIVES-2))
 (86 86 (:REWRITE SUBSET-APPEND-GIVES-1))
 (86 86 (:REWRITE |(< (- x) (- y))|))
 (48 48 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (41 41 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (8 8 (:TYPE-PRESCRIPTION GREATER-ALL))
 (4 4 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 )
(CHECK-LESS-GIVES-LESS=-MEMBER
 (3010 1505 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (2210 40 (:DEFINITION HONS-ASSOC-EQUAL))
 (2048 120 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (1505 1505 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (664 206 (:REWRITE SUBSET-SAME-MEMBERS))
 (558 158 (:REWRITE DEFAULT-CDR))
 (468 132 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (420 120 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (418 208 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (343 342 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (280 40 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (278 278 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (240 20 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (214 64 (:REWRITE PERM-WHEN-NOT-CONSP))
 (206 206 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (200 200 (:TYPE-PRESCRIPTION GOOD-TAXON-INDEX-HALIST))
 (196 40 (:DEFINITION HONS-EQUAL))
 (196 16 (:REWRITE SIMPLIFY-SUMS-<))
 (196 16 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (196 16 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (196 16 (:REWRITE DEFAULT-<-1))
 (160 16 (:REWRITE DEFAULT-<-2))
 (136 136 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (128 128 (:TYPE-PRESCRIPTION PERM))
 (125 35 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (100 100 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (60 4 (:REWRITE PERM-OF-CONSP))
 (48 4 (:REWRITE SUBSET-OF-CONSP))
 (41 41 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (41 41 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (41 41 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (41 41 (:REWRITE |(equal (- x) (- y))|))
 (39 39 (:REWRITE SUBSET-TRANSITIVE))
 (39 39 (:REWRITE SUBSET-APPEND-GIVES-2))
 (39 39 (:REWRITE SUBSET-APPEND-GIVES-1))
 (36 36 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (30 30 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (20 20 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (16 16 (:REWRITE |(< (- x) (- y))|))
 (16 4 (:REWRITE DEL-WHEN-NOT-CONSP))
 (15 15 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 )
(GET-MIN-KEY-CORRECT
 (33710 559 (:DEFINITION HONS-ASSOC-EQUAL))
 (27524 1677 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (26591 47 (:DEFINITION CHECK-LESS))
 (21695 1677 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (17118 8559 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (9582 1890 (:REWRITE SUBSET-SAME-MEMBERS))
 (8753 8753 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (5518 13 (:DEFINITION GET-MIN-KEY2))
 (5190 1404 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (4192 1893 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (3230 2210 (:REWRITE DEFAULT-CDR))
 (3182 463 (:REWRITE SUBSET-TRANSITIVE))
 (2811 2811 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (2795 559 (:DEFINITION HONS-EQUAL))
 (2776 2767 (:TYPE-PRESCRIPTION BOUND-TO-NAT-HET-NUMBER))
 (2772 738 (:REWRITE PERM-WHEN-NOT-CONSP))
 (2624 2624 (:REWRITE DEFAULT-CAR))
 (2040 510 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (1863 1863 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (1803 453 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (1670 127 (:REWRITE SIMPLIFY-SUMS-<))
 (1670 127 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1670 127 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (1670 127 (:REWRITE DEFAULT-<-1))
 (1506 1506 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (1476 1476 (:TYPE-PRESCRIPTION PERM))
 (1408 1408 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (1174 1174 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (1127 127 (:REWRITE DEFAULT-<-2))
 (1013 608 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (1013 608 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (1013 608 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (1007 32 (:REWRITE INTEGER-HALISTP-HALISTP))
 (928 49 (:DEFINITION INTEGER-HALISTP))
 (657 108 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (608 608 (:REWRITE |(equal (- x) (- y))|))
 (564 564 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (462 462 (:REWRITE SUBSET-APPEND-GIVES-2))
 (462 462 (:REWRITE SUBSET-APPEND-GIVES-1))
 (407 407 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (404 127 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (317 9 (:REWRITE PERM-OF-CONSP))
 (270 60 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (236 127 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (210 30 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (128 32 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (127 127 (:REWRITE |(< (- x) (- y))|))
 (96 96 (:REWRITE REDUCE-INTEGERP-+))
 (96 96 (:REWRITE INTEGERP-MINUS-X))
 (96 96 (:META META-INTEGERP-CORRECT))
 (58 58 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (56 56 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (36 9 (:REWRITE DEL-WHEN-NOT-CONSP))
 (32 32 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (28 28 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 )
(SUBSET-STRIP-CARS-STRIP-CARS
 (510 4 (:REWRITE PAIR-KEY-CUR-MIN-SAME-AS-GET-MIN2))
 (366 5 (:DEFINITION HONS-ASSOC-EQUAL))
 (350 15 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (216 15 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (120 84 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (97 24 (:REWRITE PERM-WHEN-NOT-CONSP))
 (84 6 (:REWRITE INTEGER-HALISTP-HALISTP))
 (68 17 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (66 6 (:DEFINITION INTEGER-HALISTP))
 (56 56 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (52 26 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (44 44 (:TYPE-PRESCRIPTION PERM))
 (40 40 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (40 32 (:REWRITE DEFAULT-CDR))
 (32 32 (:REWRITE DEFAULT-CAR))
 (28 4 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (24 6 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (23 23 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (22 22 (:REWRITE SUBSET-APPEND-GIVES-2))
 (22 22 (:REWRITE SUBSET-APPEND-GIVES-1))
 (21 3 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (21 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (21 3 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (19 19 (:REWRITE SUBSET-SAME-MEMBERS))
 (19 19 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (19 19 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (16 4 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (14 14 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (13 13 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (12 12 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (11 1 (:REWRITE PERM-OF-CONSP))
 (9 5 (:DEFINITION HONS-EQUAL))
 (6 6 (:REWRITE REDUCE-INTEGERP-+))
 (6 6 (:REWRITE INTEGERP-MINUS-X))
 (6 6 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (6 6 (:META META-INTEGERP-CORRECT))
 (4 4 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (4 4 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (4 1 (:REWRITE DEL-WHEN-NOT-CONSP))
 (3 3 (:REWRITE |(equal (- x) (- y))|))
 (2 2 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (2 2 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (2 2 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 )
(SORT-CORRECT
 (6678 88 (:DEFINITION HONS-ASSOC-EQUAL))
 (5155 231 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (5069 37 (:REWRITE PAIR-KEY-CUR-MIN-SAME-AS-GET-MIN2))
 (3643 231 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (2275 37 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (1795 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (1494 747 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (994 35 (:REWRITE ASSOC-HQUAL-FROM-MEMBER-GEN-STRIP-CARS))
 (953 953 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (879 47 (:REWRITE INTEGER-HALISTP-HALISTP))
 (811 35 (:REWRITE ASSOC-CAR-FROM-SUBSET))
 (807 213 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (749 42 (:DEFINITION INTEGER-HALISTP))
 (694 8 (:REWRITE DEFAULT-<-2))
 (568 415 (:REWRITE DEFAULT-CDR))
 (545 68 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (534 145 (:REWRITE PERM-WHEN-NOT-CONSP))
 (478 62 (:REWRITE MEMBER-GEN-CAR-STRIP-CARS))
 (454 454 (:REWRITE DEFAULT-CAR))
 (311 76 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (297 66 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (292 292 (:REWRITE SUBSET-SAME-MEMBERS))
 (292 292 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (288 288 (:TYPE-PRESCRIPTION PERM))
 (280 88 (:DEFINITION HONS-EQUAL))
 (248 68 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (248 68 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (248 68 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (231 33 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (217 217 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (171 33 (:REWRITE MEMBER-TAXA-ASSOC-HQUAL))
 (164 20 (:REWRITE CAR-STRIP-CARS-GEN))
 (143 143 (:REWRITE SUBSET-APPEND-GIVES-2))
 (143 143 (:REWRITE SUBSET-APPEND-GIVES-1))
 (136 8 (:REWRITE SIMPLIFY-SUMS-<))
 (136 8 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (136 8 (:REWRITE DEFAULT-<-1))
 (108 108 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (74 74 (:REWRITE REDUCE-INTEGERP-+))
 (74 74 (:REWRITE INTEGERP-MINUS-X))
 (74 74 (:META META-INTEGERP-CORRECT))
 (68 68 (:REWRITE |(equal (- x) (- y))|))
 (66 66 (:TYPE-PRESCRIPTION TIP-P))
 (66 9 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (53 9 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (37 37 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (37 37 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (33 33 (:REWRITE MEMBER-GIVES-ASSOC-HQUAL))
 (33 33 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (33 33 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (16 16 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (15 15 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (9 9 (:REWRITE CHECK-LESS-GIVES-LESS=-MEMBER))
 (9 2 (:REWRITE GET-MIN-KEY-CORRECT))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (8 8 (:REWRITE |(< (- x) (- y))|))
 (4 4 (:TYPE-PRESCRIPTION BOUND-TO-NAT-LIST))
 (3 3 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (2 2 (:REWRITE BOUND-TO-NAT-LIST-WHEN-NOT-CONSP))
 (2 2 (:REWRITE BOUND-TO-NAT-ATOM-DB))
 )
(ORDEREDP-CLUSTER
 (12462 160 (:DEFINITION HONS-ASSOC-EQUAL))
 (7712 105 (:REWRITE BOUND-TO-NAT-HET-NUMBER))
 (7148 384 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (5452 384 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (4701 43 (:REWRITE PAIR-KEY-CUR-MIN-SAME-AS-GET-MIN2))
 (4546 21 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (3779 21 (:REWRITE DEFAULT-<-2))
 (3348 120 (:REWRITE ASSOC-HQUAL-FROM-MEMBER-GEN-STRIP-CARS))
 (2745 120 (:REWRITE ASSOC-CAR-FROM-SUBSET))
 (2454 33 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (2380 122 (:REWRITE INTEGER-HALISTP-HALISTP))
 (2052 103 (:DEFINITION INTEGER-HALISTP))
 (1889 50 (:REWRITE MEMBER-GEN-CAR-STRIP-CARS))
 (1806 903 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (1418 1418 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (1305 901 (:REWRITE DEFAULT-CDR))
 (1217 323 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (1141 1026 (:REWRITE DEFAULT-CAR))
 (966 698 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (918 204 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (742 12 (:REWRITE CAR-STRIP-CARS-GEN))
 (736 160 (:DEFINITION HONS-EQUAL))
 (735 209 (:REWRITE PERM-WHEN-NOT-CONSP))
 (728 116 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (651 540 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (606 120 (:REWRITE MEMBER-TAXA-ASSOC-HQUAL))
 (594 139 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (496 496 (:REWRITE SUBSET-SAME-MEMBERS))
 (496 496 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (417 417 (:TYPE-PRESCRIPTION PERM))
 (396 159 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (396 159 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (396 159 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (383 122 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (359 359 (:TYPE-PRESCRIPTION MYTIPS))
 (357 21 (:REWRITE SIMPLIFY-SUMS-<))
 (357 21 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (357 21 (:REWRITE DEFAULT-<-1))
 (330 45 (:DEFINITION GET-FIRSTS))
 (328 328 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (325 325 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (306 47 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (287 75 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (232 232 (:TYPE-PRESCRIPTION TIP-P))
 (216 11 (:REWRITE CLUSTER-T-DOESNT-CHANGE-ORDERED-NIL))
 (214 214 (:REWRITE SUBSET-TRANSITIVE))
 (214 214 (:REWRITE SUBSET-APPEND-GIVES-2))
 (206 206 (:REWRITE REDUCE-INTEGERP-+))
 (206 206 (:REWRITE INTEGERP-MINUS-X))
 (206 206 (:META META-INTEGERP-CORRECT))
 (204 40 (:DEFINITION TRUE-LISTP))
 (201 186 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (172 172 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (163 163 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (159 159 (:REWRITE |(equal (- x) (- y))|))
 (149 21 (:REWRITE MEMBER-GEN-GET-TAXA-WITH-GREATER-ALL-GIVES-<CUR-MIN))
 (120 120 (:REWRITE MEMBER-GIVES-ASSOC-HQUAL))
 (97 82 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (79 43 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (69 69 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (69 33 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (63 21 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 (56 14 (:REWRITE TIP-P-GIVES-TASPIP-T))
 (55 6 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (52 52 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (50 50 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (47 47 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (45 45 (:REWRITE FIRST-TAXON-WHEN-NOT-CONSP))
 (38 2 (:REWRITE SUBSET-SUBSET-GIVES-SUBSET-APPEND))
 (36 12 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (26 2 (:REWRITE EQUAL-CAR-ASSOC-KEY))
 (23 19 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (23 1 (:REWRITE SORT-CORRECT))
 (21 21 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (21 21 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (21 21 (:REWRITE GIVES-GET-MIN-KEY-LESS-ALL-MEMBERS))
 (21 21 (:REWRITE CHECK-LESS-GIVES-LESS=-MEMBER))
 (21 21 (:REWRITE |(< (- x) (- y))|))
 (20 4 (:DEFINITION BINARY-APPEND))
 (19 19 (:REWRITE SUBSET-MYTIPS-GIVES-SUBSET-STRIP-CARS-PAIR))
 (18 18 (:REWRITE SUBSET-THROUGH-DEL-PAIR))
 (18 18 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (18 4 (:REWRITE ALISTP-GEN-SORT))
 (16 16 (:REWRITE TASPIP-STRIP-CARS-PAIR))
 (14 14 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (13 7 (:REWRITE GET-MIN-KEY-NOT-KEY-MEMBER-STRIP))
 (12 12 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (10 1 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (3 3 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 )
(TREE-LISTP-THROUGH-DEL-PAIR
 (242 32 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (148 148 (:TYPE-PRESCRIPTION STRIP-CDRS-GEN))
 (143 6 (:REWRITE LEN-GREATER-1-TREE-LISTP=TREEP))
 (132 31 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (132 31 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (62 62 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (54 54 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (54 4 (:REWRITE TREEP-AND-CONSP-LEN-AT-LEAST-2))
 (42 5 (:REWRITE MEMBER-OF-TREE-LISTP-IS-TREEP))
 (33 33 (:TYPE-PRESCRIPTION LEN))
 (31 31 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (28 4 (:DEFINITION LEN))
 (26 1 (:REWRITE NON-TIP-TREE-LISTP-OF-CONS))
 (23 5 (:REWRITE TREE-LISTP-AND-CONSP-GIVES-TREEP))
 (16 16 (:REWRITE DEFAULT-CAR))
 (14 14 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (10 10 (:TYPE-PRESCRIPTION MEMBER-GEN))
 (8 4 (:REWRITE DEFAULT-+-2))
 (6 3 (:REWRITE SIMPLIFY-SUMS-<))
 (6 3 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (6 3 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (6 3 (:REWRITE DEFAULT-<-1))
 (5 5 (:REWRITE TREEP-WHEN-NOT-CONSP))
 (5 5 (:REWRITE SUBSET-SAME-MEMBERS))
 (5 5 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (5 5 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (5 5 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (5 5 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (5 5 (:REWRITE MEMBER-GEN-X-DEL-PAIR-MEMBER-ORIGINAL))
 (5 5 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (5 5 (:REWRITE |(equal (- x) (- y))|))
 (4 4 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (4 4 (:REWRITE NORMALIZE-ADDENDS))
 (4 4 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (3 3 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE |(< (- x) (- y))|))
 )
(TREE-LISTP-THROUGH-SORT
 (1449 7 (:REWRITE PAIR-KEY-CUR-MIN-SAME-AS-GET-MIN2))
 (1070 13 (:DEFINITION HONS-ASSOC-EQUAL))
 (1061 39 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (610 39 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (476 43 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (440 4 (:REWRITE LEN-GREATER-1-TREE-LISTP=TREEP))
 (430 9 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (365 1 (:REWRITE NON-TIP-TREE-LISTP-OF-CONS))
 (160 40 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (149 38 (:REWRITE PERM-WHEN-NOT-CONSP))
 (148 74 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (144 36 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (132 132 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (111 111 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (104 104 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (102 6 (:REWRITE INTEGER-HALISTP-HALISTP))
 (98 72 (:REWRITE DEFAULT-CDR))
 (86 86 (:TYPE-PRESCRIPTION PERM))
 (84 6 (:DEFINITION INTEGER-HALISTP))
 (64 64 (:REWRITE DEFAULT-CAR))
 (61 9 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (53 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (53 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (53 8 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (45 11 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (45 11 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (41 41 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (40 40 (:TYPE-PRESCRIPTION STRIP-CDRS-GEN))
 (40 40 (:REWRITE SUBSET-APPEND-GIVES-2))
 (40 40 (:REWRITE SUBSET-APPEND-GIVES-1))
 (40 40 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (39 14 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (38 38 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (35 8 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (35 8 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (31 2 (:REWRITE TREEP-AND-CONSP-LEN-AT-LEAST-2))
 (30 30 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (25 13 (:DEFINITION HONS-EQUAL))
 (24 24 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (24 6 (:REWRITE GOOD-TAXON-INTEGER-LISTP-ALISTP-GEN))
 (24 2 (:DEFINITION LEN))
 (21 21 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (18 18 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (18 4 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (15 15 (:TYPE-PRESCRIPTION LEN))
 (14 2 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:REWRITE |(equal (- x) (- y))|))
 (8 8 (:META META-INTEGERP-CORRECT))
 (7 7 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (7 7 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (6 6 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (6 6 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (4 4 (:TYPE-PRESCRIPTION TIP-P))
 (4 4 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (4 2 (:REWRITE DEFAULT-+-2))
 (4 1 (:REWRITE ATOM-CDR-ASSOC-GOOD-TAXON-LIST))
 (3 3 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (3 3 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 (2 2 (:TYPE-PRESCRIPTION TREEP))
 (2 2 (:TYPE-PRESCRIPTION GOOD-INDEX-TAXON-HALIST))
 (2 2 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 (2 2 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (2 2 (:REWRITE NORMALIZE-ADDENDS))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 1 (:REWRITE SIMPLIFY-SUMS-<))
 (2 1 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (2 1 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (1 1 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (1 1 (:REWRITE GOOD-INDEX-TAXON-HALIST-WHEN-NOT-CONSP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE |(< (- x) (- y))|))
 )
(MEMBER-LEN-DEL-PAIR-ONE-LESS
 (155 37 (:REWRITE SUBSET-SAME-MEMBERS))
 (137 72 (:REWRITE DEFAULT-+-2))
 (79 39 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (76 19 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (72 72 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (72 72 (:REWRITE NORMALIZE-ADDENDS))
 (72 72 (:REWRITE DEFAULT-+-1))
 (60 15 (:REWRITE PERM-WHEN-NOT-CONSP))
 (60 4 (:REWRITE PERM-OF-CONSP))
 (59 26 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (56 25 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (48 4 (:REWRITE SUBSET-OF-CONSP))
 (45 45 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (45 45 (:REWRITE DEFAULT-CDR))
 (37 37 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (36 18 (:REWRITE |(equal (+ c x) d)|))
 (30 30 (:TYPE-PRESCRIPTION PERM))
 (27 27 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (26 26 (:REWRITE |(equal (- x) (- y))|))
 (24 9 (:REWRITE |(equal (+ d x) (+ c y))|))
 (24 9 (:REWRITE |(equal (+ c x) (+ d y))|))
 (24 6 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (17 17 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (16 4 (:REWRITE DEL-WHEN-NOT-CONSP))
 (10 10 (:REWRITE SUBSET-TRANSITIVE))
 (10 10 (:REWRITE SUBSET-APPEND-GIVES-2))
 (10 10 (:REWRITE SUBSET-APPEND-GIVES-1))
 )
(LEN-SORT-BY-INSERTION
 (1194 5 (:REWRITE PAIR-KEY-CUR-MIN-SAME-AS-GET-MIN2))
 (847 27 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (818 9 (:DEFINITION HONS-ASSOC-EQUAL))
 (487 27 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (465 32 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (130 33 (:REWRITE PERM-WHEN-NOT-CONSP))
 (106 53 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (104 26 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (100 6 (:REWRITE INTEGER-HALISTP-HALISTP))
 (83 6 (:DEFINITION INTEGER-HALISTP))
 (81 81 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (79 79 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (78 61 (:REWRITE DEFAULT-CDR))
 (75 75 (:TYPE-PRESCRIPTION PERM))
 (53 9 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (50 8 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (46 46 (:REWRITE DEFAULT-CAR))
 (35 35 (:REWRITE SUBSET-APPEND-GIVES-2))
 (35 35 (:REWRITE SUBSET-APPEND-GIVES-1))
 (33 33 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (33 8 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (30 30 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (28 28 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (27 6 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (22 11 (:REWRITE DEFAULT-+-2))
 (21 3 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (19 19 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (13 9 (:DEFINITION HONS-EQUAL))
 (12 3 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (11 11 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (11 11 (:REWRITE NORMALIZE-ADDENDS))
 (11 11 (:REWRITE DEFAULT-+-1))
 (9 9 (:REWRITE |(equal (- x) (- y))|))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:META META-INTEGERP-CORRECT))
 (7 7 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (6 6 (:TYPE-PRESCRIPTION TIP-P))
 (6 6 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (5 5 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (5 5 (:REWRITE ALISTP-GEN-OF-NOT-CONSP))
 (4 4 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (4 2 (:REWRITE |(equal (+ c x) d)|))
 (1 1 (:REWRITE NOT-MEMBER-THROUGH-DEL-PAIR))
 (1 1 (:REWRITE ALISTP-GEN-THROUGH-DEL-PAIR))
 )
(LEN-CLUSTER-SORT
 (686 78 (:REWRITE PERM-IMPLIES-SUBSET))
 (355 55 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (320 70 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (294 73 (:REWRITE PERM-WHEN-NOT-CONSP))
 (271 197 (:REWRITE DEFAULT-CDR))
 (266 4 (:REWRITE PAIR-KEY-CUR-MIN-SAME-AS-GET-MIN2))
 (243 47 (:DEFINITION TRUE-LISTP))
 (235 3 (:DEFINITION HONS-ASSOC-EQUAL))
 (220 110 (:REWRITE DEFAULT-+-2))
 (219 9 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (195 195 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (188 63 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (188 63 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (188 63 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (141 141 (:TYPE-PRESCRIPTION PERM))
 (125 125 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (124 9 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (110 110 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (110 110 (:REWRITE NORMALIZE-ADDENDS))
 (110 110 (:REWRITE DEFAULT-+-1))
 (63 63 (:TYPE-PRESCRIPTION STRIP-CARS-GEN))
 (63 63 (:REWRITE SUBSET-APPEND-GIVES-2))
 (63 63 (:REWRITE |(equal (- x) (- y))|))
 (58 48 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (56 56 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (55 55 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (52 2 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (49 35 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (47 1 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (42 42 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (42 12 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (40 13 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (39 11 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (38 34 (:REWRITE DEFAULT-CAR))
 (37 3 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (36 9 (:REWRITE TIP-P-GIVES-TASPIP-T))
 (32 16 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (29 29 (:TYPE-PRESCRIPTION TIP-P))
 (25 25 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (24 12 (:REWRITE |(equal (+ c x) d)|))
 (24 2 (:REWRITE PERM-OF-CONSP))
 (21 21 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (19 1 (:REWRITE SUBSET-SUBSET-GIVES-SUBSET-APPEND))
 (18 18 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (18 6 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (16 16 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (16 14 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (15 15 (:REWRITE SUBSET-SAME-MEMBERS))
 (15 15 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (15 15 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (10 10 (:REWRITE SUBSET-MYTIPS-GIVES-SUBSET-STRIP-CARS-PAIR))
 (10 2 (:DEFINITION BINARY-APPEND))
 (9 9 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:META META-INTEGERP-CORRECT))
 (8 4 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (8 4 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (8 2 (:REWRITE DEL-WHEN-NOT-CONSP))
 (7 3 (:DEFINITION HONS-EQUAL))
 (6 6 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (6 6 (:REWRITE SIMPLIFY-TERMS-SUCH-AS-A+AB-=-0))
 (6 6 (:REWRITE |(equal (- x) 0)|))
 (3 3 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (3 3 (:REWRITE TASPIP-STRIP-CARS-PAIR))
 (3 3 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 )
(TREE-LISTP-THROUGH-CLUSTER-SORT
 (1862 230 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (1306 144 (:REWRITE PERM-IMPLIES-SUBSET))
 (1106 14 (:DEFINITION HONS-ASSOC-EQUAL))
 (1074 7 (:REWRITE PAIR-KEY-CUR-MIN-SAME-AS-GET-MIN2))
 (887 42 (:REWRITE NOT-MEMBER-NOT-CONSP-ASSOC))
 (816 30 (:REWRITE LEN-GREATER-1-TREE-LISTP=TREEP))
 (641 221 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (594 11 (:REWRITE NON-TIP-TREE-LISTP-OF-CONS))
 (557 146 (:REWRITE PERM-WHEN-NOT-CONSP))
 (530 42 (:REWRITE NOT-CONSP-ASSOC-NOT-ASSOC-HQUAL))
 (455 75 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (450 46 (:REWRITE NOT-MEMBER-SUBSET))
 (439 439 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (402 91 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (357 31 (:REWRITE MEMBER-OF-TREE-LISTP-IS-TREEP))
 (312 65 (:DEFINITION TRUE-LISTP))
 (288 191 (:REWRITE DEFAULT-CDR))
 (284 284 (:TYPE-PRESCRIPTION PERM))
 (240 240 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (237 237 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (205 89 (:REWRITE SUBSET-SAME-MEMBERS))
 (173 78 (:TYPE-PRESCRIPTION INTEGER-ASSOC-HQUAL-INTEGER-HALISTP))
 (172 46 (:REWRITE MEMBER-GEN-WHEN-NOT-CONS))
 (155 107 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (150 94 (:REWRITE STRIP-CARS-GEN-WHEN-NOT-CONSP))
 (149 32 (:REWRITE TREE-LISTP-AND-CONSP-GIVES-TREEP))
 (144 144 (:REWRITE SUBSET-TRANSITIVE))
 (144 144 (:REWRITE SUBSET-APPEND-GIVES-2))
 (129 89 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (128 104 (:REWRITE DEFAULT-CAR))
 (110 110 (:TYPE-PRESCRIPTION HONS-ASSOC-EQUAL))
 (108 8 (:REWRITE PERM-OF-CONSP))
 (100 100 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (96 20 (:DEFINITION LEN))
 (89 89 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (84 84 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (78 78 (:TYPE-PRESCRIPTION INTEGER-HALISTP))
 (75 75 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (75 75 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (52 10 (:REWRITE MEMBER-GEN-ALISTP-GEN-GIVES-CONSP))
 (46 46 (:REWRITE PROPER-SUBTREE-MEMBER-GEN))
 (46 10 (:REWRITE SIMPLIFY-SUMS-EQUAL))
 (46 10 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-EQUAL))
 (46 10 (:REWRITE PREFER-POSITIVE-ADDENDS-EQUAL))
 (44 39 (:REWRITE PAIR-KEY-WITH-VALUE-WHEN-NOT-CONSP))
 (40 10 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (38 14 (:DEFINITION HONS-EQUAL))
 (38 6 (:REWRITE STRIP-CDRS-GEN-WHEN-NOT-CONSP))
 (32 8 (:REWRITE DEL-WHEN-NOT-CONSP))
 (27 3 (:REWRITE CONSP-THROUGH-STRIP-CDRS))
 (26 5 (:REWRITE ATOM-CDR-ASSOC-GOOD-TAXON-LIST))
 (24 2 (:REWRITE CONSP-GIVES-CONSP-SORT))
 (20 10 (:REWRITE DEFAULT-+-2))
 (19 7 (:REWRITE GET-MIN-KEY-WHEN-NOT-CONSP))
 (19 1 (:REWRITE SUBSET-SUBSET-GIVES-SUBSET-APPEND))
 (18 6 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (16 16 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (16 8 (:REWRITE SIMPLIFY-SUMS-<))
 (16 8 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (16 8 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (16 8 (:REWRITE DEFAULT-<-1))
 (15 3 (:REWRITE GOOD-INDEX-TAXON-HALIST-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION SORT-THE-ALIST-BY-INSERTION))
 (10 10 (:REWRITE REDUCE-INTEGERP-+))
 (10 10 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (10 10 (:REWRITE NORMALIZE-ADDENDS))
 (10 10 (:REWRITE INTEGERP-MINUS-X))
 (10 10 (:REWRITE DEFAULT-+-1))
 (10 10 (:REWRITE |(equal (- x) (- y))|))
 (10 10 (:META META-INTEGERP-CORRECT))
 (10 2 (:REWRITE DEL-PAIR-WHEN-NOT-CONSP))
 (9 9 (:TYPE-PRESCRIPTION STRIP-CDRS-GEN))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (8 8 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (8 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE |(< (- x) (- y))|))
 (6 6 (:TYPE-PRESCRIPTION GOOD-INDEX-TAXON-HALIST))
 (6 6 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (3 3 (:REWRITE SUBSET-MYTIPS-GIVES-SUBSET-STRIP-CARS-PAIR))
 (2 2 (:REWRITE TASPIP-STRIP-CARS-PAIR))
 (2 2 (:REWRITE SORT-THE-ALIST-BY-INSERTION-WHEN-NOT-CONSP))
 )
(TREEP-CLUSTER
 (1583 168 (:DEFINITION LEN))
 (952 56 (:REWRITE |(< (+ c x) d)|))
 (711 107 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (578 73 (:REWRITE PERM-IMPLIES-SUBSET))
 (432 216 (:REWRITE DEFAULT-+-2))
 (359 359 (:TYPE-PRESCRIPTION MYTIPS))
 (353 319 (:REWRITE DEFAULT-CDR))
 (276 67 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (270 63 (:REWRITE PERM-WHEN-NOT-CONSP))
 (261 48 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (248 107 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (218 50 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (216 216 (:REWRITE NORMALIZE-TERMS-SUCH-AS-A/A+B-+-B/A+B))
 (216 216 (:REWRITE NORMALIZE-ADDENDS))
 (216 216 (:REWRITE DEFAULT-+-1))
 (206 206 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (204 102 (:REWRITE DEFAULT-<-1))
 (203 102 (:REWRITE SIMPLIFY-SUMS-<))
 (203 102 (:REWRITE SIMPLIFY-PRODUCTS-GATHER-EXPONENTS-<))
 (203 102 (:REWRITE PREFER-POSITIVE-ADDENDS-<))
 (200 2 (:REWRITE NON-TIP-TREE-LISTP-OF-CONS))
 (174 33 (:DEFINITION TRUE-LISTP))
 (158 158 (:REWRITE REMOVE-WEAK-INEQUALITIES-TWO))
 (158 158 (:REWRITE REMOVE-WEAK-INEQUALITIES-ONE))
 (138 138 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (137 137 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (134 105 (:REWRITE TREE-LISTP-WHEN-NOT-CONSP))
 (126 126 (:TYPE-PRESCRIPTION PERM))
 (102 102 (:REWRITE DEFAULT-<-2))
 (102 102 (:REWRITE |(< (- x) (- y))|))
 (74 74 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (73 73 (:REWRITE SUBSET-TRANSITIVE))
 (66 66 (:REWRITE SUBSET-SAME-MEMBERS))
 (66 66 (:REWRITE MEMBER-PERM-GIVES-MEMBER))
 (66 66 (:REWRITE MEMBER-DIFFERENCE-MEMBER))
 (50 50 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (48 48 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (38 38 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (38 38 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (38 14 (:REWRITE TIP-P-GIVES-TASPIP-T))
 (38 10 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (38 2 (:REWRITE SUBSET-SUBSET-GIVES-SUBSET-APPEND))
 (36 12 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (27 27 (:REWRITE DEFAULT-CAR))
 (26 26 (:TYPE-PRESCRIPTION TIP-P))
 (20 4 (:DEFINITION BINARY-APPEND))
 (14 14 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (12 12 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (8 8 (:REWRITE REDUCE-INTEGERP-+))
 (8 8 (:REWRITE INTEGERP-MINUS-X))
 (8 8 (:META META-INTEGERP-CORRECT))
 (4 4 (:DEFINITION NULL))
 )
(SUBSET-MYTIPS-THROUGH-ORDER)
(TASPIP-THROUGH-ORDER
 (184 30 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (138 17 (:REWRITE PERM-IMPLIES-SUBSET))
 (115 19 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (96 96 (:TYPE-PRESCRIPTION MYTIPS))
 (71 13 (:DEFINITION TRUE-LISTP))
 (69 17 (:REWRITE PERM-WHEN-NOT-CONSP))
 (61 61 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (37 37 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (33 33 (:TYPE-PRESCRIPTION PERM))
 (19 19 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (17 17 (:REWRITE SUBSET-TRANSITIVE))
 (17 17 (:REWRITE SUBSET-APPEND-GIVES-2))
 (17 17 (:REWRITE SUBSET-APPEND-GIVES-1))
 (17 17 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (15 3 (:REWRITE TIP-P-GIVES-TASPIP-T))
 (14 14 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (14 14 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (13 4 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (12 12 (:REWRITE DEFAULT-CDR))
 (9 2 (:REWRITE TIP-P-NOT-INTEGER-GIVES-SYMBOLP))
 (8 8 (:TYPE-PRESCRIPTION TIP-P))
 (4 4 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (3 3 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (2 2 (:REWRITE REDUCE-INTEGERP-+))
 (2 2 (:REWRITE INTEGERP-MINUS-X))
 (2 2 (:META META-INTEGERP-CORRECT))
 )
(ORDER-BY-INSERTION-GIVES-ORDEREDP
 (15 2 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (9 1 (:REWRITE PERM-IMPLIES-SUBSET))
 (8 1 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (6 6 (:TYPE-PRESCRIPTION MYTIPS))
 (5 5 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (5 1 (:DEFINITION TRUE-LISTP))
 (4 1 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (4 1 (:REWRITE PERM-WHEN-NOT-CONSP))
 (2 2 (:TYPE-PRESCRIPTION PERM))
 (2 2 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (2 2 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (2 2 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (1 1 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (1 1 (:REWRITE SUBSET-TRANSITIVE))
 (1 1 (:REWRITE SUBSET-APPEND-GIVES-2))
 (1 1 (:REWRITE SUBSET-APPEND-GIVES-1))
 (1 1 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (1 1 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (1 1 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE CLUSTER-SORT-BY-INSERTION-WHEN-NOT-CONSP))
 )
(ORDER-BY-INSERTION-GIVES-TREEP)
(ORDER-BY-INSERTION-GIVES-TREE-LISTP
 (32 5 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (26 6 (:REWRITE TREE-LIST-LISTP-TREE-LISTP))
 (26 3 (:REWRITE PERM-IMPLIES-SUBSET))
 (16 2 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (13 3 (:REWRITE PERM-WHEN-NOT-CONSP))
 (12 12 (:TYPE-PRESCRIPTION MYTIPS))
 (10 10 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (10 10 (:TYPE-PRESCRIPTION NON-TIP-TREE-LISTP))
 (10 6 (:REWRITE NON-TIP-TREE-LISTP-WHEN-NOT-CONSP))
 (10 2 (:DEFINITION TRUE-LISTP))
 (6 6 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (5 5 (:TYPE-PRESCRIPTION PERM))
 (4 4 (:REWRITE TASPIP-CLUSTER-SORT-BY-INSERTION))
 (4 4 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (3 3 (:TYPE-PRESCRIPTION GET-TAXA-FROM-TAXON-INDEX))
 (3 3 (:REWRITE SUBSET-TRANSITIVE))
 (3 3 (:REWRITE SUBSET-APPEND-GIVES-2))
 (3 3 (:REWRITE SUBSET-APPEND-GIVES-1))
 (3 3 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (3 3 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (3 3 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (2 2 (:REWRITE TREE-LISTP-THROUGH-CLUSTER-SORT))
 (2 2 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (2 2 (:REWRITE DEFAULT-CDR))
 )
(ORDER-EACH-BY-INSERTION
 (129 23 (:REWRITE GOOD-INDEX-FLATTEN-TASPIP))
 (125 26 (:REWRITE TASPIP-NIL-AND-CONSP-GIVES-TASPIP-FLG))
 (116 11 (:REWRITE PERM-IMPLIES-SUBSET))
 (83 16 (:DEFINITION TRUE-LISTP))
 (71 71 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (53 11 (:REWRITE PERM-WHEN-NOT-CONSP))
 (49 10 (:REWRITE SUBSET-WHEN-NOT-CONS))
 (26 26 (:REWRITE TASPIP-WHEN-NOT-CONSP))
 (25 25 (:REWRITE MYTIPS-WHEN-NOT-CONSP))
 (24 24 (:REWRITE DEFAULT-CDR))
 (23 23 (:REWRITE TASPIP-FLG-CONSP-GIVES-TASPIP-NIL))
 (23 23 (:REWRITE GET-TAXA-FROM-TAXON-INDEX-WHEN-NOT-CONSP))
 (22 22 (:TYPE-PRESCRIPTION PERM))
 (18 6 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (12 3 (:REWRITE TIP-P-GIVES-TASPIP-T))
 (11 11 (:REWRITE SUBSET-TRANSITIVE))
 (11 11 (:REWRITE SUBSET-APPEND-GIVES-2))
 (11 11 (:REWRITE NOT-INTERSECT-TOPS-NOT-SUBSET))
 (10 2 (:DEFINITION BINARY-APPEND))
 (8 8 (:REWRITE GREATER-ALL-WHEN-NOT-CONSP))
 (8 8 (:REWRITE GOOD-TAXON-INDEX-HALIST-WHEN-NOT-CONSP))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 6 (:TYPE-PRESCRIPTION TIP-P))
 (6 6 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (3 3 (:REWRITE TIP-P-WHEN-NOT-CONSP))
 (3 3 (:REWRITE TASPIP-FLG-AND-FLG-GIVES-T))
 (1 1 (:REWRITE SUBSET-SUBSET-GIVES-SUBSET-APPEND))
 )
