(TERM-GRAPH-P-ST)
(BOUNDED-TERM-GRAPH-P-FIX-TRUE-LISTP
 (363 121 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (355 301 (:REWRITE DEFAULT-CAR))
 (147 141 (:REWRITE DEFAULT-CDR))
 (64 34 (:REWRITE DEFAULT-<-2))
 (34 34 (:REWRITE DEFAULT-<-1))
 (34 34 (:META CANCEL_PLUS-LESSP-CORRECT))
 (32 32 (:REWRITE NATP-RW))
 (30 30 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (18 18 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (18 18 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(TERM-GRAPH-P-FIX-TRUE-LISTP
 (228 2 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (150 10 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (90 10 (:DEFINITION EMPTY-GRAPH-P-REC))
 (60 60 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (60 20 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (50 50 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (32 2 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (31 31 (:REWRITE DEFAULT-CAR))
 (30 10 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (27 27 (:REWRITE DEFAULT-CDR))
 (18 18 (:TYPE-PRESCRIPTION LEN))
 (10 2 (:DEFINITION LEN))
 (8 4 (:REWRITE DEFAULT-<-2))
 (8 2 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (4 4 (:REWRITE NATP-RW))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 2 (:REWRITE DEFAULT-+-2))
 (3 1 (:DEFINITION TRUE-LIST-FIX))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(TERM-GRAPH-P-ST-MAIN-PROPERTY)
(QUASI-TERM-GRAPH-P-FIX-TRUE-LISTP
 (220 190 (:REWRITE DEFAULT-CAR))
 (126 120 (:REWRITE DEFAULT-CDR))
 (73 73 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (56 56 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (38 38 (:REWRITE NATP-RW))
 (18 18 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (18 18 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(LIST-OF-TERM-DAG-VARIABLES-ST
 (114 1 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (75 5 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (45 5 (:DEFINITION EMPTY-GRAPH-P-REC))
 (39 1 (:DEFINITION QUASI-TERM-GRAPH-P))
 (31 31 (:REWRITE DEFAULT-CAR))
 (30 30 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (30 10 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (29 29 (:REWRITE DEFAULT-CDR))
 (25 25 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (16 1 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (15 5 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (15 3 (:DEFINITION LEN))
 (10 2 (:DEFINITION NAT-TRUE-LISTP))
 (6 3 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE NATP-RW))
 (4 4 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (4 4 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (4 2 (:REWRITE DEFAULT-<-2))
 (4 2 (:DEFINITION DAGP))
 (4 1 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 2 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 )
(LIST-OF-TERM-DAG-VARIABLES-FIX-TRUE-LISTP
 (57 51 (:REWRITE DEFAULT-CAR))
 (44 40 (:REWRITE DEFAULT-CDR))
 (14 14 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (14 14 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(LIST-OF-TERM-DAG-VARIABLES-ST-MAIN-PROPERTY)
(QUASI-TERM-GRAPH-P-NTH
 (94 94 (:REWRITE DEFAULT-CAR))
 (80 16 (:DEFINITION NAT-TRUE-LISTP))
 (56 56 (:REWRITE DEFAULT-CDR))
 (32 32 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (24 24 (:REWRITE NATP-RW))
 (18 18 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (11 11 (:REWRITE ZP-OPEN))
 (8 8 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (8 8 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 )
(NEIGHBORS-ST
 (244 2 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (157 11 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (92 11 (:DEFINITION EMPTY-GRAPH-P-REC))
 (64 64 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (63 21 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (51 51 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (48 2 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (46 46 (:REWRITE DEFAULT-CAR))
 (40 40 (:REWRITE DEFAULT-CDR))
 (35 7 (:DEFINITION LEN))
 (33 11 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (24 2 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (19 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE NATP-RW))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:META CANCEL_PLUS-LESSP-CORRECT))
 (5 5 (:REWRITE ZP-OPEN))
 (4 4 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (4 2 (:DEFINITION TRUE-LISTP))
 (4 2 (:DEFINITION DAGP))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 )
(EQUAL-NEIGHBORS-ST-NEIGHBORS)
(BOUNDED-TERM-GRAPH-P-CONTENTS
 (144 144 (:REWRITE DEFAULT-CAR))
 (117 39 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (110 110 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (92 7 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (60 1 (:DEFINITION QUASI-TERM-GRAPH-P))
 (48 16 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (47 24 (:REWRITE DEFAULT-<-2))
 (27 27 (:REWRITE NATP-RW))
 (24 24 (:REWRITE DEFAULT-<-1))
 (24 24 (:META CANCEL_PLUS-LESSP-CORRECT))
 (23 23 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (19 19 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (18 2 (:DEFINITION NAT-TRUE-LISTP))
 (17 17 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (17 17 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (13 13 (:REWRITE ZP-OPEN))
 (12 12 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (10 10 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (8 8 (:REWRITE DEFAULT-+-2))
 (8 8 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 )
(DAG-P-AUX-ST
 (5104 8 (:DEFINITION DAG-P-AUX-ST))
 (4713 41 (:DEFINITION MEMBER-EQUAL))
 (2544 69 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (1980 33 (:DEFINITION QUASI-TERM-GRAPH-P))
 (1443 1443 (:REWRITE DEFAULT-CAR))
 (1285 257 (:REWRITE ZP-OPEN))
 (1099 77 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (1009 1009 (:REWRITE DEFAULT-CDR))
 (644 77 (:DEFINITION EMPTY-GRAPH-P-REC))
 (594 66 (:DEFINITION NAT-TRUE-LISTP))
 (465 465 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (448 448 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (441 147 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (382 338 (:REWRITE DEFAULT-<-2))
 (357 357 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (355 306 (:REWRITE DEFAULT-+-2))
 (339 338 (:REWRITE DEFAULT-<-1))
 (338 338 (:META CANCEL_PLUS-LESSP-CORRECT))
 (330 330 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (306 306 (:REWRITE DEFAULT-+-1))
 (245 49 (:DEFINITION LEN))
 (234 234 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (231 77 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (169 169 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (169 169 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (162 14 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (132 132 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (66 66 (:TYPE-PRESCRIPTION NATP))
 (34 17 (:DEFINITION TRUE-LISTP))
 (10 5 (:DEFINITION DAGP))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(EQUAL-DAG-P-AUX-ST-DAG-P-AUX
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 (6006 115 (:DEFINITION QUASI-TERM-GRAPH-P))
 (2179 2179 (:REWRITE DEFAULT-CDR))
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 (1315 1315 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (990 990 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
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 (692 692 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (626 617 (:REWRITE DEFAULT-<-1))
 (617 617 (:REWRITE DEFAULT-<-2))
 (617 617 (:META CANCEL_PLUS-LESSP-CORRECT))
 (600 600 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (396 396 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
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 (279 279 (:REWRITE DEFAULT-+-2))
 (279 279 (:REWRITE DEFAULT-+-1))
 (198 198 (:TYPE-PRESCRIPTION NATP))
 (9 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (2 2 (:REWRITE NTH-0-CONS))
 )
(BOUNDED-NAT-LISTP-LIST-OF-N
 (22 22 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (15 9 (:REWRITE DEFAULT-<-1))
 (14 9 (:REWRITE DEFAULT-<-2))
 (10 8 (:REWRITE DEFAULT-CAR))
 (9 9 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (9 9 (:META CANCEL_PLUS-LESSP-CORRECT))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (5 4 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE ZP-OPEN))
 (3 3 (:REWRITE NATP-RW))
 )
(DAG-P-ST
 (15 3 (:DEFINITION LEN))
 (6 3 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-CDR))
 (4 4 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-+-1))
 (2 1 (:DEFINITION DAGP))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:DEFINITION TERM-GRAPH-P))
 )
(EQUAL-DAG-P-ST-DAG-P
 (270 3 (:DEFINITION DAG-P-AUX))
 (234 3 (:DEFINITION NEIGHBORS))
 (192 3 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (180 3 (:DEFINITION QUASI-TERM-GRAPH-P))
 (54 6 (:DEFINITION NAT-TRUE-LISTP))
 (45 45 (:REWRITE DEFAULT-CAR))
 (42 42 (:REWRITE DEFAULT-CDR))
 (39 39 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (30 30 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (18 18 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (15 3 (:REWRITE ZP-OPEN))
 (15 3 (:DEFINITION LEN))
 (12 12 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (12 3 (:DEFINITION NFIX))
 (9 9 (:REWRITE NATP-RW))
 (9 6 (:REWRITE DEFAULT-+-2))
 (7 7 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (7 7 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:TYPE-PRESCRIPTION LIST-OF-N))
 (6 6 (:REWRITE DEFAULT-<-2))
 (6 6 (:REWRITE DEFAULT-<-1))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 6 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3 3 (:TYPE-PRESCRIPTION LEN))
 (3 3 (:DEFINITION MEMBER-EQUAL))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 )
(WELL-FORMED-TERM-DAG-ST-P
 (114 1 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (75 5 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (45 5 (:DEFINITION EMPTY-GRAPH-P-REC))
 (30 30 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (30 10 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (25 25 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (23 23 (:REWRITE DEFAULT-CAR))
 (20 20 (:REWRITE DEFAULT-CDR))
 (16 1 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (15 5 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (11 1 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
 (10 2 (:DEFINITION LEN))
 (4 2 (:REWRITE DEFAULT-<-2))
 (4 2 (:REWRITE DEFAULT-+-2))
 (4 1 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:REWRITE NATP-RW))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 1 (:DEFINITION TRUE-LISTP))
 (2 1 (:DEFINITION DAGP))
 (1 1 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (1 1 (:REWRITE DAG-P-COMPLETENESS))
 )
(WELL-FORMED-TERM-DAG-ST-P-MAIN-PROPERTY
 (396 28 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (231 28 (:DEFINITION EMPTY-GRAPH-P-REC))
 (162 162 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (159 53 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (128 128 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (119 5 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (108 108 (:REWRITE DEFAULT-CAR))
 (89 89 (:REWRITE DEFAULT-CDR))
 (84 28 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (66 5 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (40 8 (:DEFINITION LEN))
 (36 3 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (33 3 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
 (18 9 (:REWRITE DEFAULT-<-2))
 (16 8 (:REWRITE DEFAULT-+-2))
 (15 3 (:DEFINITION MEMBER-EQUAL))
 (12 12 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (12 12 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (10 10 (:REWRITE NATP-RW))
 (9 9 (:REWRITE DEFAULT-<-1))
 (9 9 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 8 (:REWRITE DEFAULT-+-1))
 (6 6 (:TYPE-PRESCRIPTION LIST-OF-TERM-DAG-VARIABLES))
 (5 5 (:REWRITE DAG-P-COMPLETENESS))
 (3 3 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 )
(WELL-FORMED-UPL-ST)
(WELL-FORMED-UPL-ST-MAIN-PROPERTY
 (260 2 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (170 170 (:REWRITE DEFAULT-CAR))
 (164 12 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (111 111 (:REWRITE DEFAULT-CDR))
 (94 12 (:DEFINITION EMPTY-GRAPH-P-REC))
 (68 68 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (66 22 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (64 2 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (60 12 (:DEFINITION LEN))
 (52 52 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (46 31 (:REWRITE DEFAULT-<-2))
 (40 2 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (36 12 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (36 2 (:DEFINITION TERM-GRAPH-P))
 (31 31 (:REWRITE NATP-RW))
 (31 31 (:REWRITE DEFAULT-<-1))
 (31 31 (:META CANCEL_PLUS-LESSP-CORRECT))
 (24 12 (:REWRITE DEFAULT-+-2))
 (24 2 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (22 2 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
 (12 12 (:REWRITE DEFAULT-+-1))
 (10 2 (:DEFINITION MEMBER-EQUAL))
 (7 7 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (7 7 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION LIST-OF-TERM-DAG-VARIABLES))
 (2 2 (:TYPE-PRESCRIPTION TERM-GRAPH-P))
 (2 2 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 )
(WELL-FORMED-DAG-SYSTEM-ST)
(DAG-AS-TERM-ST
 (1640 120 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (940 120 (:DEFINITION EMPTY-GRAPH-P-REC))
 (720 12 (:DEFINITION QUASI-TERM-GRAPH-P))
 (680 680 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (660 220 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (626 626 (:REWRITE DEFAULT-CAR))
 (561 561 (:REWRITE DEFAULT-CDR))
 (520 520 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (398 20 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (376 8 (:DEFINITION DAG-AS-TERM-ST))
 (360 120 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (358 20 (:DEFINITION TERM-GRAPH-P))
 (335 67 (:DEFINITION LEN))
 (216 24 (:DEFINITION NAT-TRUE-LISTP))
 (155 88 (:REWRITE DEFAULT-+-2))
 (120 120 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (117 61 (:REWRITE DEFAULT-<-2))
 (110 10 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
 (88 88 (:REWRITE DEFAULT-+-1))
 (73 73 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (73 73 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (62 61 (:REWRITE DEFAULT-<-1))
 (61 61 (:META CANCEL_PLUS-LESSP-CORRECT))
 (50 10 (:DEFINITION MEMBER-EQUAL))
 (48 48 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (37 21 (:REWRITE ZP-OPEN))
 (31 31 (:REWRITE DAG-P-COMPLETENESS))
 (20 20 (:TYPE-PRESCRIPTION TERM-GRAPH-P))
 (18 9 (:DEFINITION TRUE-LISTP))
 (18 9 (:DEFINITION DAGP))
 (1 1 (:TYPE-PRESCRIPTION EQLABLEP))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(EQUAL-DAG-AS-TERM-ST-DAG-AS-TERM-L
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 (660 11 (:DEFINITION QUASI-TERM-GRAPH-P))
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 (143 143 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
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 (133 133 (:REWRITE DEFAULT-CAR))
 (110 110 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (66 66 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (44 44 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (33 33 (:REWRITE NATP-RW))
 (30 30 (:REWRITE DAG-P-COMPLETENESS))
 (27 27 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (27 27 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (22 22 (:TYPE-PRESCRIPTION NATP))
 )
(TBS-AS-SYSTEM-ST
 (390 3 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (246 18 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (152 152 (:REWRITE DEFAULT-CAR))
 (141 18 (:DEFINITION EMPTY-GRAPH-P-REC))
 (110 22 (:DEFINITION LEN))
 (105 105 (:REWRITE DEFAULT-CDR))
 (102 102 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (99 33 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (96 3 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (78 78 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (60 3 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (54 18 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (54 3 (:DEFINITION TERM-GRAPH-P))
 (44 22 (:REWRITE DEFAULT-+-2))
 (38 22 (:REWRITE DEFAULT-<-2))
 (36 3 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (33 3 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
 (24 22 (:REWRITE DEFAULT-<-1))
 (22 22 (:REWRITE DEFAULT-+-1))
 (22 22 (:META CANCEL_PLUS-LESSP-CORRECT))
 (20 20 (:REWRITE NATP-RW))
 (15 3 (:DEFINITION MEMBER-EQUAL))
 (12 12 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (12 12 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 6 (:TYPE-PRESCRIPTION LIST-OF-TERM-DAG-VARIABLES))
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 (3 3 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (3 3 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (3 3 (:REWRITE DAG-P-COMPLETENESS))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(EQUAL-TBS-AS-SYSTEM-ST-TBS-AS-SYSTEM
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 (768 12 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (720 12 (:DEFINITION QUASI-TERM-GRAPH-P))
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 (142 142 (:REWRITE DEFAULT-CDR))
 (120 120 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (72 72 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (48 48 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
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 (27 27 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (27 27 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (24 24 (:TYPE-PRESCRIPTION NATP))
 (12 12 (:TYPE-PRESCRIPTION DAG-P))
 (12 12 (:REWRITE DAG-P-COMPLETENESS))
 )
(SOLVED-AS-SYSTEM-ST
 (260 2 (:DEFINITION BOUNDED-TERM-GRAPH-P))
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 (94 12 (:DEFINITION EMPTY-GRAPH-P-REC))
 (81 81 (:REWRITE DEFAULT-CAR))
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 (68 68 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (66 22 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (64 2 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (52 52 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (40 2 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (36 12 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (36 2 (:DEFINITION TERM-GRAPH-P))
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 (22 2 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
 (20 10 (:REWRITE DEFAULT-<-2))
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(UPL-AS-PAIR-OF-SYSTEMS-ST)
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(EQUAL-OCCUR-CHECK-ST-OCCUR-CHECK-ST
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(NTH-0-CAR
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 (40 40 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (40 2 (:DEFINITION PAIR-ARGS))
 (32 8 (:REWRITE NATP-DAG-DEREF-L-BOUNDED-TERM-GRAPH-P))
 (32 3 (:DEFINITION UPDATE-NTH))
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 (24 24 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (20 20 (:REWRITE NATP-RW))
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 (17 17 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (16 16 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (16 16 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (12 12 (:REWRITE DEFAULT-<-2))
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 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
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 (12 12 (:DEFINITION NOT))
 (10 2 (:DEFINITION BINARY-APPEND))
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 (6 6 (:REWRITE DAG-P-COMPLETENESS))
 (2 2 (:REWRITE DAG-DEREF-L-NOT-TERM-DAG-IS-P))
 )
(DAG-TRANSFORM-MM-ST-SECOND-COMPONENT
 (308 4 (:DEFINITION DAG-DEREF-L))
 (256 4 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (240 4 (:DEFINITION QUASI-TERM-GRAPH-P))
 (134 88 (:REWRITE DEFAULT-CAR))
 (124 10 (:DEFINITION NTH))
 (114 84 (:REWRITE DEFAULT-CDR))
 (92 12 (:REWRITE ZP-OPEN))
 (72 8 (:DEFINITION NAT-TRUE-LISTP))
 (52 52 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (44 2 (:DEFINITION OCCUR-CHECK-L))
 (40 40 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (40 2 (:DEFINITION PAIR-ARGS))
 (32 8 (:REWRITE NATP-DAG-DEREF-L-BOUNDED-TERM-GRAPH-P))
 (32 3 (:DEFINITION UPDATE-NTH))
 (24 24 (:TYPE-PRESCRIPTION NATP))
 (24 24 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (20 20 (:REWRITE NATP-RW))
 (17 17 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (17 17 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (16 16 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (16 16 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (12 12 (:REWRITE DEFAULT-<-2))
 (12 12 (:REWRITE DEFAULT-<-1))
 (12 12 (:REWRITE DEFAULT-+-2))
 (12 12 (:REWRITE DEFAULT-+-1))
 (12 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 12 (:DEFINITION NOT))
 (10 2 (:DEFINITION BINARY-APPEND))
 (6 6 (:TYPE-PRESCRIPTION DAG-P))
 (6 6 (:REWRITE DAG-P-COMPLETENESS))
 (2 2 (:REWRITE DAG-DEREF-L-NOT-TERM-DAG-IS-P))
 )
(DAG-TRANSFORM-MM-ST-THIRD-COMPONENT
 (462 6 (:DEFINITION DAG-DEREF-L))
 (384 6 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (360 6 (:DEFINITION QUASI-TERM-GRAPH-P))
 (186 15 (:DEFINITION NTH))
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 (163 126 (:REWRITE DEFAULT-CDR))
 (138 18 (:REWRITE ZP-OPEN))
 (108 12 (:DEFINITION NAT-TRUE-LISTP))
 (78 78 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (66 3 (:DEFINITION OCCUR-CHECK-L))
 (60 60 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (60 3 (:DEFINITION PAIR-ARGS))
 (48 12 (:REWRITE NATP-DAG-DEREF-L-BOUNDED-TERM-GRAPH-P))
 (47 4 (:DEFINITION UPDATE-NTH))
 (36 36 (:TYPE-PRESCRIPTION NATP))
 (36 36 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (30 30 (:REWRITE NATP-RW))
 (24 24 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (24 24 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (24 24 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (24 24 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (18 18 (:REWRITE DEFAULT-<-2))
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 (15 3 (:DEFINITION BINARY-APPEND))
 (9 9 (:TYPE-PRESCRIPTION DAG-P))
 (9 9 (:REWRITE DAG-P-COMPLETENESS))
 (3 3 (:REWRITE DAG-DEREF-L-NOT-TERM-DAG-IS-P))
 )
(DAG-TRANSFORM-MM-ST-FOURTH-COMPONENT
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 (1980 33 (:DEFINITION QUASI-TERM-GRAPH-P))
 (666 57 (:DEFINITION NTH))
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 (573 539 (:REWRITE DEFAULT-CAR))
 (528 503 (:REWRITE DEFAULT-CDR))
 (444 64 (:REWRITE ZP-OPEN))
 (429 429 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (330 330 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (198 198 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (132 132 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (130 130 (:REWRITE NATP-RW))
 (128 128 (:TYPE-PRESCRIPTION NATP))
 (124 31 (:REWRITE NATP-DAG-DEREF-L-BOUNDED-TERM-GRAPH-P))
 (64 64 (:REWRITE DEFAULT-<-2))
 (64 64 (:REWRITE DEFAULT-<-1))
 (64 64 (:REWRITE DEFAULT-+-2))
 (64 64 (:REWRITE DEFAULT-+-1))
 (64 64 (:META CANCEL_PLUS-LESSP-CORRECT))
 (60 3 (:DEFINITION PAIR-ARGS))
 (47 47 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (47 47 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (37 37 (:REWRITE DAG-P-COMPLETENESS))
 (29 29 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (15 3 (:DEFINITION BINARY-APPEND))
 )
(WELL-FORMED-UPL-LIST
 (260 2 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (164 12 (:REWRITE EMPTY-GRAPH-P-REC-BOUNDED-TERM-GRAPH-P))
 (94 12 (:DEFINITION EMPTY-GRAPH-P-REC))
 (75 75 (:REWRITE DEFAULT-CAR))
 (68 68 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (67 67 (:REWRITE DEFAULT-CDR))
 (66 22 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (64 2 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (52 52 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
 (46 2 (:DEFINITION BOUNDED-NAT-PAIRS-TRUE-LISTP))
 (40 2 (:REWRITE BOUNDED-TERM-GRAPH-P-PARTICULAR-CASE))
 (36 36 (:TYPE-PRESCRIPTION LEN))
 (36 12 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (36 2 (:DEFINITION TERM-GRAPH-P))
 (30 2 (:DEFINITION BOUNDED-NAT-SUBSTITUTION-P))
 (24 2 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (22 2 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
 (20 4 (:DEFINITION LEN))
 (18 10 (:REWRITE DEFAULT-<-2))
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 (10 10 (:REWRITE DEFAULT-<-1))
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 (10 2 (:DEFINITION MEMBER-EQUAL))
 (8 4 (:REWRITE DEFAULT-+-2))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION LIST-OF-TERM-DAG-VARIABLES))
 (4 4 (:REWRITE DEFAULT-+-1))
 (2 2 (:TYPE-PRESCRIPTION TERM-GRAPH-P))
 (2 2 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (2 2 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 )
(WELL-FORMED-UPL-ST-PRESERVED-BY-DAG-TRANSFORM-MM-ST-CASI
 (28 13 (:REWRITE DEFAULT-CAR))
 (27 9 (:REWRITE DEFAULT-CDR))
 (18 18 (:TYPE-PRESCRIPTION DAG-TRANSFORM-MM-L))
 )
(WELL-FORMED-UPL-ST-PRESERVED-BY-DAG-TRANSFORM-MM-ST
 (110 41 (:REWRITE DEFAULT-CAR))
 (98 37 (:REWRITE DEFAULT-CDR))
 (48 48 (:TYPE-PRESCRIPTION DAG-TRANSFORM-MM-L))
 (29 5 (:REWRITE DAG-TRANSFORM-MM-ST-FOURTH-COMPONENT))
 (12 3 (:REWRITE DAG-TRANSFORM-MM-ST-THIRD-COMPONENT))
 )
(UPL-AS-PAIR-OF-SYSTEM-LIST
 (498 6 (:DEFINITION DAG-AS-TERM-L))
 (384 6 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (360 6 (:DEFINITION QUASI-TERM-GRAPH-P))
 (344 2 (:DEFINITION TBS-AS-SYSTEM))
 (178 2 (:DEFINITION SOLVED-AS-SYSTEM))
 (108 12 (:DEFINITION NAT-TRUE-LISTP))
 (99 93 (:REWRITE DEFAULT-CAR))
 (95 89 (:REWRITE DEFAULT-CDR))
 (78 78 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (60 60 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
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 (30 6 (:REWRITE ZP-OPEN))
 (24 24 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (18 18 (:REWRITE NATP-RW))
 (12 12 (:TYPE-PRESCRIPTION NATP))
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 (12 12 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (12 12 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 6 (:TYPE-PRESCRIPTION DAG-P))
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 (6 6 (:REWRITE DEFAULT-+-2))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 6 (:REWRITE DAG-P-COMPLETENESS))
 (6 6 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(UNIFICATION-MEASURE-DECREASES-ST
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 (231 90 (:REWRITE DEFAULT-CDR))
 (67 16 (:REWRITE DEFAULT-<-2))
 (47 15 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (44 16 (:REWRITE DEFAULT-<-1))
 (16 16 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (16 16 (:META CANCEL_PLUS-LESSP-CORRECT))
 (16 16 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(DAG-SOLVE-SYSTEM-ST
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 (1509 1315 (:REWRITE DEFAULT-CAR))
 (1437 180 (:DEFINITION EMPTY-GRAPH-P-REC))
 (1282 1099 (:REWRITE DEFAULT-CDR))
 (1020 1020 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
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 (942 30 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (780 780 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
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 (540 180 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (536 30 (:DEFINITION TERM-GRAPH-P))
 (435 85 (:DEFINITION LEN))
 (355 177 (:REWRITE DEFAULT-<-2))
 (226 20 (:DEFINITION LIST-OF-TERM-DAG-VARIABLES))
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 (165 165 (:REWRITE NATP-RW))
 (100 20 (:DEFINITION MEMBER-EQUAL))
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 (92 92 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (85 85 (:REWRITE DEFAULT-+-1))
 (40 16 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (30 30 (:TYPE-PRESCRIPTION TERM-GRAPH-P))
 (25 25 (:REWRITE DAG-P-COMPLETENESS))
 (20 10 (:DEFINITION TRUE-LISTP))
 (20 10 (:DEFINITION DAGP))
 )
(TRUE-LISTP-OF-THREE-ELEMENTS)
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 (640 10 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (600 10 (:DEFINITION QUASI-TERM-GRAPH-P))
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 (176 24 (:REWRITE ZP-OPEN))
 (130 130 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (100 100 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
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 (56 14 (:REWRITE NATP-DAG-DEREF-L-BOUNDED-TERM-GRAPH-P))
 (48 48 (:TYPE-PRESCRIPTION NATP))
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 (40 40 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (40 2 (:DEFINITION PAIR-ARGS))
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 (18 18 (:META CANCEL_TIMES-EQUAL-CORRECT))
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 )
(TRUE-LISTP-OF-THREE-ELEMENTS-ELIMINATE-DESTRUCTORS
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 )
(DAG-SOLVE-SYSTEM-ST-FIRST-COMPONENT
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 (10 2 (:REWRITE WELL-FORMED-UPL-PRESERVED-BY-DAG-TRANSFORM-MM-L))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION NORMAL-FORM-SYST))
 )
(DAG-SOLVE-SYSTEM-ST-SECOND-COMPONENT
 (604 233 (:REWRITE DEFAULT-CDR))
 (10 2 (:REWRITE WELL-FORMED-UPL-PRESERVED-BY-DAG-TRANSFORM-MM-L))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION NORMAL-FORM-SYST))
 )
(DAG-SOLVE-SYSTEM-ST-FOURTH-COMPONENT
 (660 259 (:REWRITE DEFAULT-CDR))
 (10 2 (:REWRITE WELL-FORMED-UPL-PRESERVED-BY-DAG-TRANSFORM-MM-L))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION NORMAL-FORM-SYST))
 )
(DAG-SOLVE-SYSTEM-ST-THIRD-COMPONENT
 (363 144 (:REWRITE DEFAULT-CDR))
 (10 2 (:REWRITE WELL-FORMED-UPL-PRESERVED-BY-DAG-TRANSFORM-MM-L))
 (2 2 (:TYPE-PRESCRIPTION NORMAL-FORM-SYST))
 )
(DAG-MGS-ST)
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 (150 3 (:DEFINITION DAG-SOLVE-SYSTEM-ST))
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 (87 36 (:REWRITE DEFAULT-CAR))
 (45 45 (:TYPE-PRESCRIPTION DAG-TRANSFORM-MM-ST))
 (33 3 (:REWRITE DAG-TRANSFORM-MM-ST-SECOND-COMPONENT))
 (29 29 (:TYPE-PRESCRIPTION DAG-TRANSFORM-MM-L))
 (24 3 (:REWRITE MV-NTH-0-FIRST))
 (21 3 (:REWRITE DAG-TRANSFORM-MM-ST-FIRST-COMPONENT))
 (21 3 (:DEFINITION SOLVE-UPL-L))
 (15 1 (:REWRITE DAG-SOLVE-SYSTEM-ST-THIRD-COMPONENT))
 (9 3 (:REWRITE WELL-FORMED-UPL-ST-MAIN-PROPERTY))
 (9 3 (:DEFINITION NORMAL-FORM-SYST))
 (7 7 (:TYPE-PRESCRIPTION WELL-FORMED-UPL))
 (3 1 (:REWRITE TRUE-LISTP-OF-THREE-ELEMENTS-ELIMINATE-DESTRUCTORS))
 (2 2 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-THREE-ELEMENTS))
 )
(DAG-MGS-ST-THIRD-COMPONENT
 (150 3 (:DEFINITION DAG-SOLVE-SYSTEM-ST))
 (101 43 (:REWRITE DEFAULT-CDR))
 (90 39 (:REWRITE DEFAULT-CAR))
 (45 45 (:TYPE-PRESCRIPTION DAG-TRANSFORM-MM-ST))
 (33 3 (:REWRITE DAG-TRANSFORM-MM-ST-SECOND-COMPONENT))
 (29 29 (:TYPE-PRESCRIPTION DAG-TRANSFORM-MM-L))
 (26 4 (:DEFINITION SOLVE-UPL-L))
 (24 3 (:REWRITE MV-NTH-0-FIRST))
 (21 3 (:REWRITE DAG-TRANSFORM-MM-ST-FIRST-COMPONENT))
 (15 1 (:REWRITE DAG-SOLVE-SYSTEM-ST-THIRD-COMPONENT))
 (12 4 (:DEFINITION NORMAL-FORM-SYST))
 (9 3 (:REWRITE WELL-FORMED-UPL-ST-MAIN-PROPERTY))
 (8 8 (:TYPE-PRESCRIPTION WELL-FORMED-UPL))
 (3 1 (:REWRITE TRUE-LISTP-OF-THREE-ELEMENTS-ELIMINATE-DESTRUCTORS))
 (2 2 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-THREE-ELEMENTS))
 )
(DAG-MGS-ST-SECOND-COMPONENT
 (200 4 (:DEFINITION DAG-SOLVE-SYSTEM-ST))
 (107 41 (:REWRITE DEFAULT-CDR))
 (99 42 (:REWRITE DEFAULT-CAR))
 (73 1 (:REWRITE DAG-SOLVE-SYSTEM-ST-SECOND-COMPONENT))
 (60 60 (:TYPE-PRESCRIPTION DAG-TRANSFORM-MM-ST))
 (44 4 (:REWRITE DAG-TRANSFORM-MM-ST-SECOND-COMPONENT))
 (38 38 (:TYPE-PRESCRIPTION DAG-TRANSFORM-MM-L))
 (32 4 (:REWRITE MV-NTH-0-FIRST))
 (28 4 (:REWRITE DAG-TRANSFORM-MM-ST-FIRST-COMPONENT))
 (12 4 (:REWRITE WELL-FORMED-UPL-ST-MAIN-PROPERTY))
 (3 1 (:REWRITE TRUE-LISTP-OF-THREE-ELEMENTS-ELIMINATE-DESTRUCTORS))
 (2 2 (:TYPE-PRESCRIPTION TRUE-LISTP-OF-THREE-ELEMENTS))
 )
(EMPTY-GRAPH-P-ST)
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 (8 7 (:REWRITE DEFAULT-CDR))
 (6 6 (:REWRITE ZP-OPEN))
 (5 5 (:REWRITE DEFAULT-+-2))
 (5 5 (:REWRITE DEFAULT-+-1))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2))
 (1 1 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 )
(EMPTY-GRAPH-P-FIX-TRUE-LISTP
 (25 25 (:REWRITE DEFAULT-CAR))
 (19 19 (:REWRITE DEFAULT-CDR))
 (15 5 (:DEFINITION TRUE-LIST-FIX))
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 (10 10 (:REWRITE DEFAULT-+-1))
 (10 10 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(EMPTY-GRAPH-P-ST-MAIN-PROPERTY
 (32 2 (:DEFINITION LIST-FROM-TO))
 (30 2 (:DEFINITION EMPTY-GRAPH-P-AUX))
 (20 2 (:DEFINITION NTH))
 (18 4 (:REWRITE ZP-OPEN))
 (14 2 (:REWRITE COMMUTATIVITY-OF-+))
 (12 12 (:TYPE-PRESCRIPTION LEN))
 (12 8 (:REWRITE DEFAULT-+-2))
 (10 8 (:REWRITE DEFAULT-+-1))
 (10 2 (:DEFINITION LEN))
 (7 7 (:REWRITE DEFAULT-CDR))
 (7 7 (:REWRITE DEFAULT-CAR))
 (6 2 (:REWRITE UNICITY-OF-0))
 (4 4 (:TYPE-PRESCRIPTION LIST-FROM-TO))
 (4 4 (:DEFINITION NOT))
 (4 2 (:DEFINITION FIX))
 (3 1 (:DEFINITION TRUE-LIST-FIX))
 (2 2 (:REWRITE POSITIVE-LEN))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
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 (30 6 (:DEFINITION INTEGER-ABS))
 (24 6 (:REWRITE COMMUTATIVITY-OF-+))
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 (6 6 (:TYPE-PRESCRIPTION ALISTP))
 (6 6 (:REWRITE DEFAULT-UNARY-MINUS))
 (6 6 (:REWRITE DEFAULT-CAR))
 (3 3 (:TYPE-PRESCRIPTION LEN))
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 (3 3 (:REWRITE INTEGERP==>DENOMINATOR=1))
 (3 3 (:REWRITE DEFAULT-REALPART))
 (3 3 (:REWRITE DEFAULT-NUMERATOR))
 (3 3 (:REWRITE DEFAULT-IMAGPART))
 (3 3 (:REWRITE DEFAULT-DENOMINATOR))
 (3 3 (:REWRITE DEFAULT-COERCE-2))
 (3 3 (:REWRITE DEFAULT-COERCE-1))
 )
(TERM-AS-DAG)
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 (184 23 (:DEFINITION VAL))
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 (60 60 (:TYPE-PRESCRIPTION NATP))
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 (45 45 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
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 (527 55 (:DEFINITION EMPTY-GRAPH-P-REC))
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 (471 7 (:REWRITE MV-NTH-2-THIRD))
 (422 2 (:DEFINITION UPDATE-DAGI))
 (420 2 (:DEFINITION UPDATE-NTH-ARRAY))
 (338 222 (:REWRITE DEFAULT-CDR))
 (330 330 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (330 110 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (325 223 (:REWRITE DEFAULT-CAR))
 (275 275 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
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 (165 55 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (154 154 (:TYPE-PRESCRIPTION LEN))
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(BOUNDED-NAT-SUBSTITUTION-P-ASSOC-CONSP
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 (20 20 (:REWRITE DEFAULT-CDR))
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 (7 7 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (22 22 (:REWRITE DEFAULT-CDR))
 (14 8 (:REWRITE DEFAULT-<-2))
 (8 8 (:REWRITE DEFAULT-<-1))
 (8 8 (:META CANCEL_PLUS-LESSP-CORRECT))
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 )
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 (1319 877 (:REWRITE DEFAULT-CDR))
 (1115 727 (:REWRITE DEFAULT-CAR))
 (959 538 (:REWRITE DEFAULT-+-2))
 (750 75 (:DEFINITION UPDATE-NTH))
 (692 136 (:DEFINITION LEN))
 (610 538 (:REWRITE DEFAULT-+-1))
 (473 31 (:DEFINITION BOUNDED-NAT-SUBSTITUTION-P))
 (286 26 (:REWRITE MV-NTH-2-THIRD))
 (228 111 (:REWRITE DEFAULT-<-2))
 (225 25 (:REWRITE ASSOC-VAL))
 (200 25 (:DEFINITION VAL))
 (187 96 (:TYPE-PRESCRIPTION ASSOC-CONSP-OR-NIL))
 (185 111 (:REWRITE DEFAULT-<-1))
 (182 26 (:DEFINITION ASSOC-EQUAL))
 (111 111 (:META CANCEL_PLUS-LESSP-CORRECT))
 (75 75 (:REWRITE ZP-OPEN))
 (73 73 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (73 73 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (69 57 (:REWRITE NATP-RW))
 (44 44 (:REWRITE FOLD-CONSTS-IN-+))
 (44 22 (:DEFINITION TRUE-LISTP))
 (44 22 (:DEFINITION DAGP))
 (25 25 (:DEFINITION ACONS))
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 (4 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(TERM-AS-DAG
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 (90 10 (:DEFINITION EMPTY-GRAPH-P-REC))
 (60 60 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (60 20 (:REWRITE EMPTY-GRAPH-P-EMPTY-GRAPH-P-REC))
 (50 50 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P-REC))
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 (40 8 (:DEFINITION LEN))
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 (22 11 (:REWRITE DEFAULT-+-2))
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 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (14 14 (:REWRITE DEFAULT-+-1))
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 (11 11 (:REWRITE DEFAULT-<-1))
 (9 3 (:REWRITE FOLD-CONSTS-IN-+))
 (8 8 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
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 (2 2 (:REWRITE NATP-RW))
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(LEN-RESIZE-LIST
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 (18 18 (:REWRITE DEFAULT-+-1))
 (17 3 (:REWRITE CONSP-RESIZE-LIST))
 (14 14 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 10 (:REWRITE DEFAULT-CDR))
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 (11 11 (:REWRITE DEFAULT-<-1))
 (9 3 (:REWRITE FOLD-CONSTS-IN-+))
 (5 5 (:REWRITE NATP-RW))
 (5 5 (:REWRITE DEFAULT-CAR))
 (3 3 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:REWRITE EQUAL-CONSTANT-+))
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(UNIF-TWO-TERMS-PROBLEM-ST
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 (22 16 (:REWRITE DEFAULT-+-1))
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 (12 12 (:REWRITE DEFAULT-CAR))
 (5 1 (:DEFINITION LEN))
 (3 3 (:REWRITE FOLD-CONSTS-IN-+))
 (3 1 (:REWRITE EMPTY-GRAPH-P-IMPLIES-BOUNDED-TERM-GRAPH-P))
 (2 1 (:DEFINITION TRUE-LISTP))
 (2 1 (:DEFINITION DAGP))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(UNIF-TWO-TERMS-PROBLEM-ST-UNIF-TWO-TERMS-PROBLEM-L
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 (20 4 (:DEFINITION LENGTH-TERM))
 (5 5 (:REWRITE DEFAULT-CDR))
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 (3 3 (:REWRITE DEFAULT-CAR))
 )
(INITIAL-TO-BE-SOLVED-ST)
(INITIAL-TO-BE-SOLVED-ST-INITIAL-TO-BE-SOLVED-L
 (10 10 (:REWRITE DEFAULT-CAR))
 (5 5 (:REWRITE DEFAULT-CDR))
 )
(DAG-MGU-ST)
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 (2187 2187 (:REWRITE DEFAULT-<-2))
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 (1458 1458 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1458 1458 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(SEVERAL-PROPERTIES-UNIF-TWO-TERMS-PROBLEM-L
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 (40 8 (:DEFINITION LENGTH-TERM))
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 (8 8 (:REWRITE FOLD-CONSTS-IN-+))
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(DAG-MGU-ST
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 (10 8 (:REWRITE DEFAULT-CDR))
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 (5 1 (:DEFINITION LEN))
 (2 1 (:REWRITE DEFAULT-+-2))
 (2 1 (:DEFINITION TRUE-LISTP))
 (2 1 (:DEFINITION DAGP))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(DAG-MGU-ST-FIRST-COMPONENT
 (12 2 (:REWRITE DAG-MGS-L-COMPLETENESS))
 (8 8 (:REWRITE DEFAULT-CAR))
 (6 4 (:REWRITE DEFAULT-CDR))
 (6 2 (:REWRITE UNIF-TWO-TERMS-PROBLEM-L-WELL-FORMED-DAG-SYSTEM))
 (4 4 (:TYPE-PRESCRIPTION WELL-FORMED-UPL))
 (4 4 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 )
(DAG-MGU-ST-THIRD-COMPONENT
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 (12 9 (:REWRITE DEFAULT-CAR))
 (12 2 (:REWRITE DAG-MGS-L-COMPLETENESS))
 (6 2 (:REWRITE UNIF-TWO-TERMS-PROBLEM-L-WELL-FORMED-DAG-SYSTEM))
 (4 4 (:TYPE-PRESCRIPTION WELL-FORMED-UPL))
 (4 4 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
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(DAG-MGU-ST-SECOND-COMPONENT
 (18 3 (:REWRITE DAG-MGS-L-COMPLETENESS))
 (9 3 (:REWRITE UNIF-TWO-TERMS-PROBLEM-L-WELL-FORMED-DAG-SYSTEM))
 (6 6 (:TYPE-PRESCRIPTION WELL-FORMED-UPL))
 (6 6 (:TYPE-PRESCRIPTION EMPTY-GRAPH-P))
 (4 4 (:REWRITE DEFAULT-CAR))
 (2 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:TYPE-PRESCRIPTION DAG-MGS-ST))
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(DAG-MGU-AUX)
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 (46 27 (:REWRITE DEFAULT-CDR))
 (38 25 (:REWRITE DEFAULT-CAR))
 (22 4 (:DEFINITION LEN))
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 (8 4 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-+-1))
 (4 2 (:DEFINITION TRUE-LISTP))
 (4 2 (:DEFINITION DAGP))
 (3 3 (:REWRITE DAG-MGU-L-COMPLETENESS))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
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(DAG-MGU)
(DAG-MGS-ST-COMPLETENESS
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 (128 2 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (120 2 (:DEFINITION QUASI-TERM-GRAPH-P))
 (43 41 (:REWRITE DEFAULT-CAR))
 (36 34 (:REWRITE DEFAULT-CDR))
 (36 4 (:DEFINITION NAT-TRUE-LISTP))
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 (10 2 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
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 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
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(DAG-MGS-ST-SOUNDNESS
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 (119 100 (:REWRITE DEFAULT-CDR))
 (108 12 (:DEFINITION NAT-TRUE-LISTP))
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 (30 6 (:REWRITE ZP-OPEN))
 (30 1 (:DEFINITION SOLUTION))
 (24 24 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (22 4 (:REWRITE DAG-MGS-ST-COMPLETENESS))
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 (12 12 (:TYPE-PRESCRIPTION NATP))
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(DAG-MGS-ST-IDEMPOTENT
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(DAG-MGS-ST-MOST-GENERAL-SOLUTION
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 (36 36 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (32 4 (:DEFINITION VAL))
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 (22 4 (:REWRITE DAG-MGS-ST-COMPLETENESS))
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 (12 12 (:TYPE-PRESCRIPTION NATP))
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(DAG-MGU-ST-COMPLETENESS
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 (16 2 (:DEFINITION VAL))
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 (8 8 (:REWRITE DEFAULT-CDR))
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 (3 3 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(DAG-MGU-ST-SOUNDNESS
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 (44 4 (:DEFINITION APPLY-SUBST))
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 (20 4 (:REWRITE ZP-OPEN))
 (16 16 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
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 (12 12 (:REWRITE NATP-RW))
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 (8 8 (:TYPE-PRESCRIPTION NATP))
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 (7 7 (:REWRITE DAG-MGU-ST-COMPLETENESS))
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 (4 4 (:REWRITE DEFAULT-+-1))
 (4 4 (:REWRITE DAG-P-COMPLETENESS))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
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(DAG-MGU-ST-MOST-GENERAL-SOLUTION
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 (32 4 (:DEFINITION VAL))
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 (10 10 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (6 6 (:REWRITE NATP-RW))
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 (2 2 (:REWRITE DEFAULT-+-1))
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(DAG-MGU-ST-IDEMPOTENT
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 (36 4 (:DEFINITION NAT-TRUE-LISTP))
 (26 26 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (22 2 (:DEFINITION NTH))
 (20 20 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (12 12 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
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 (10 2 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (8 6 (:REWRITE DAG-MGU-L-COMPLETENESS))
 (6 6 (:REWRITE NATP-RW))
 (5 5 (:REWRITE DAG-MGU-ST-COMPLETENESS))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (4 4 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION DAG-P))
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 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
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(DAG-MGU-COMPLETENESS
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 (176 2 (:DEFINITION DAG-AS-TERM-L))
 (134 2 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (126 2 (:DEFINITION QUASI-TERM-GRAPH-P))
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 (92 65 (:REWRITE DEFAULT-CDR))
 (66 6 (:DEFINITION APPLY-SUBST))
 (48 6 (:DEFINITION VAL))
 (36 4 (:DEFINITION NAT-TRUE-LISTP))
 (26 26 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
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 (13 13 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (13 13 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 12 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (10 2 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (6 6 (:REWRITE NATP-RW))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (2 2 (:TYPE-PRESCRIPTION DAG-P))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
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(DAG-MGU-SOUNDNESS
 (274 3 (:DEFINITION SOLVED-AS-SYSTEM))
 (254 3 (:DEFINITION DAG-AS-TERM-L))
 (195 3 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (183 3 (:DEFINITION QUASI-TERM-GRAPH-P))
 (101 77 (:REWRITE DEFAULT-CDR))
 (97 78 (:REWRITE DEFAULT-CAR))
 (54 6 (:DEFINITION NAT-TRUE-LISTP))
 (48 4 (:REWRITE DAG-MGU-L-COMPLETENESS))
 (47 9 (:DEFINITION TERM-P-AUX))
 (39 39 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (32 3 (:DEFINITION NTH))
 (30 30 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (22 2 (:DEFINITION APPLY-SUBST))
 (18 18 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (16 2 (:DEFINITION VAL))
 (15 3 (:REWRITE ZP-OPEN))
 (12 12 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (9 9 (:REWRITE NATP-RW))
 (8 8 (:TYPE-PRESCRIPTION EQLABLEP))
 (8 8 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (8 8 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (6 6 (:TYPE-PRESCRIPTION NATP))
 (6 6 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (3 3 (:TYPE-PRESCRIPTION DAG-P))
 (3 3 (:REWRITE DEFAULT-<-2))
 (3 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE DEFAULT-+-1))
 (3 3 (:REWRITE DAG-P-COMPLETENESS))
 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 (2 2 (:REWRITE DAG-MGU-ST-COMPLETENESS))
 )
(DAG-MGU-MOST-GENERAL-SOLUTION
 (192 2 (:DEFINITION SOLVED-AS-SYSTEM))
 (176 2 (:DEFINITION DAG-AS-TERM-L))
 (134 2 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (126 2 (:DEFINITION QUASI-TERM-GRAPH-P))
 (103 71 (:REWRITE DEFAULT-CAR))
 (97 67 (:REWRITE DEFAULT-CDR))
 (66 6 (:DEFINITION APPLY-SUBST))
 (48 6 (:DEFINITION VAL))
 (36 4 (:DEFINITION NAT-TRUE-LISTP))
 (26 26 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (24 2 (:DEFINITION NTH))
 (20 20 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (18 6 (:DEFINITION TERM-P-AUX))
 (13 13 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (13 13 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 12 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (10 2 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (6 6 (:REWRITE NATP-RW))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (2 2 (:TYPE-PRESCRIPTION DAG-P))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(DAG-MGU-IDEMPOTENT
 (185 2 (:DEFINITION SOLVED-AS-SYSTEM))
 (171 2 (:DEFINITION DAG-AS-TERM-L))
 (131 2 (:REWRITE QUASI-TERM-GRAPH-P-NTH))
 (123 2 (:DEFINITION QUASI-TERM-GRAPH-P))
 (78 52 (:REWRITE DEFAULT-CDR))
 (77 50 (:REWRITE DEFAULT-CAR))
 (36 4 (:DEFINITION NAT-TRUE-LISTP))
 (26 26 (:TYPE-PRESCRIPTION QUASI-TERM-GRAPH-P))
 (22 2 (:DEFINITION NTH))
 (20 20 (:TYPE-PRESCRIPTION NAT-TRUE-LISTP))
 (18 6 (:DEFINITION TERM-P-AUX))
 (12 12 (:REWRITE BOUNDED-TERM-GRAPH-P-IMPLIES-QUASI-TERM-GRAPH-P))
 (10 2 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE BOUNDED-NAT-TRUE-LISTP-NAT-TRUE-LISTP))
 (8 4 (:REWRITE DAG-MGU-L-COMPLETENESS))
 (6 6 (:REWRITE NATP-RW))
 (4 4 (:TYPE-PRESCRIPTION NATP))
 (4 4 (:REWRITE BOUNDED-TERM-GRAPH-P-NON-INTEGER-CONTENTS))
 (4 4 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:TYPE-PRESCRIPTION DAG-P))
 (2 2 (:REWRITE DEFAULT-<-2))
 (2 2 (:REWRITE DEFAULT-<-1))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 (2 2 (:REWRITE DAG-MGU-ST-COMPLETENESS))
 (2 2 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:DEFINITION IDEMPOTENT))
 )
