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(KEYS)
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(FIND-2NODE)
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(ST-FILTER-1MARKED-NODES)
(A-EQUAL)
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 (87 6 (:REWRITE REMOVE-EQUAL-NON-MEMBER-EQUAL))
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 (9 1 (:REWRITE MEMBER-ST-FILTER-UNMARKED123-NODES))
 (4 4 (:TYPE-PRESCRIPTION NODES-LENGTH))
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(SPEC-OF-ST-FILTER-UNMARKED123-NODES
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 (76 19 (:REWRITE O-P-O-INFP-CAR))
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 (50 50 (:REWRITE DEFAULT-CDR))
 (48 48 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
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 (36 36 (:REWRITE DEFAULT-CAR))
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 (28 12 (:REWRITE ZP-OPEN))
 (19 19 (:REWRITE O-P-DEF-O-FINP-1))
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(FORCED--NUMBER-OF-UNMARKED-NODES-DECREASES-IN-STEP-1
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 (9925 539 (:REWRITE NTH-WITH-LARGE-INDEX))
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 (1936 20 (:REWRITE DEPI-UPDATE-MARKSI))
 (1848 12 (:DEFINITION APPEND-TO-ESC))
 (1826 61 (:DEFINITION MEMBER-EQUAL))
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(3-MARKED-NOT-IN-ST-FILTER-UNMARKED123-NODES
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(FORCED--NODE-UNMARKED-AFTER-FIRST-RECURSIVE-CALL
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(FIND-2NODE-UPDATE-DEPI
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(A-DESTS-E-2NEIGHBOR-UPDATE-DEPI
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(INVARIANT-ESCS2-APPEND-TO-DEP
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 (24 24 (:REWRITE MEMBER-SUBSETP))
 (24 24 (:REWRITE CONSP-ESCI-->ESCI))
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(FIND-2NODE-UPDATE-MARKSI-1
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(A-DESTS-E-2NEIGHBOR-UPDATE-MARKSI-1
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 (332 332 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
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 (273 273 (:LINEAR LEQ-POSITION-EQUAL-LEN))
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 (192 32 (:DEFINITION MEMBER-EQUAL))
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 (91 91 (:TYPE-PRESCRIPTION ST-FILTER-NEIGHBORS-FOR-DEST))
 (80 80 (:TYPE-PRESCRIPTION UPDATE-MARKSI))
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 (16 16 (:TYPE-PRESCRIPTION NATP))
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(INVARIANT-ESCS2-UPDATE-MARKSI-1
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(ASSOC-KEY-YEILDS-FIELD
 (87 74 (:REWRITE DEFAULT-CDR))
 (76 19 (:REWRITE O-P-O-INFP-CAR))
 (61 61 (:REWRITE MEMBER-SUBSETP))
 (46 46 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (46 46 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (19 19 (:REWRITE O-P-DEF-O-FINP-1))
 )
(FIND-2NODE-IN-NEIGHBORS-IF-NEIGHBORS-IS-MARKED-2
 (1925 22 (:DEFINITION A-VALID-NODES))
 (1650 22 (:DEFINITION NODESI))
 (1364 66 (:REWRITE NTH-WITH-LARGE-INDEX))
 (1056 11 (:DEFINITION A-VALID-NODES-VALUES))
 (836 44 (:DEFINITION NTH))
 (803 481 (:REWRITE DEFAULT-CAR))
 (682 682 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (602 428 (:REWRITE DEFAULT-CDR))
 (495 126 (:REWRITE O-P-O-INFP-CAR))
 (396 396 (:TYPE-PRESCRIPTION LEN))
 (330 66 (:DEFINITION LEN))
 (317 18 (:REWRITE FIND-2NODE-UPDATE-MARKSI-2))
 (246 246 (:TYPE-PRESCRIPTION O-P))
 (242 44 (:DEFINITION NFIX))
 (234 168 (:REWRITE DEFAULT-<-2))
 (210 14 (:DEFINITION IS-KEYS-OF-ALIST))
 (196 14 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (190 190 (:META CANCEL_PLUS-LESSP-CORRECT))
 (190 168 (:REWRITE DEFAULT-<-1))
 (154 88 (:REWRITE DEFAULT-+-2))
 (132 132 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (132 132 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (123 123 (:REWRITE O-P-DEF-O-FINP-1))
 (110 22 (:REWRITE ZP-OPEN))
 (110 11 (:DEFINITION TRUE-LISTP-VALUES))
 (88 88 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (88 88 (:REWRITE DEFAULT-+-1))
 (88 22 (:REWRITE <-+-NEGATIVE-0-1))
 (84 12 (:DEFINITION ALISTP))
 (72 72 (:REWRITE NATP-RW))
 (66 66 (:TYPE-PRESCRIPTION NFIX))
 (66 66 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (64 64 (:REWRITE CONSP-NEIGHBORS<->NEIGHBORS))
 (55 22 (:DEFINITION TRUE-LISTP))
 (46 46 (:REWRITE A-VALID-NODES-IMPLIES-A-NATP))
 (22 22 (:TYPE-PRESCRIPTION A-VALID-NODES))
 (14 14 (:REWRITE SUBSETP-TRANS))
 (14 14 (:REWRITE NEIGHBORS-ARE-KEYS-OF-NEIGHBORS->DESTSI))
 (14 14 (:REWRITE A-NATP-ST-FILTER-NEIGHBORS-FOR-DEST))
 (11 11 (:TYPE-PRESCRIPTION TRUE-LISTP-VALUES))
 (11 11 (:TYPE-PRESCRIPTION A-VALID-NODES-VALUES))
 (2 2 (:REWRITE REWRITE-A-NATP-KEYS))
 )
(REWRITE-MEMBER-KEYS
 (148 69 (:REWRITE DEFAULT-CAR))
 (134 134 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (76 19 (:REWRITE O-P-O-INFP-CAR))
 (34 34 (:REWRITE MEMBER-SUBSETP))
 (31 29 (:REWRITE DEFAULT-CDR))
 (23 23 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (23 23 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (19 19 (:REWRITE O-P-DEF-O-FINP-1))
 )
(A-DESTS-E-2NEIGHBOR-UPDATE-MARKSI-2
 (3325 38 (:DEFINITION A-VALID-NODES))
 (2850 38 (:DEFINITION NODESI))
 (2356 114 (:REWRITE NTH-WITH-LARGE-INDEX))
 (1824 19 (:DEFINITION A-VALID-NODES-VALUES))
 (1651 1063 (:REWRITE DEFAULT-CAR))
 (1559 131 (:REWRITE FIND-2NODE-UPDATE-MARKSI-2))
 (1444 76 (:DEFINITION NTH))
 (1307 1307 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (1275 51 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
 (1071 102 (:DEFINITION A-NATP))
 (964 241 (:REWRITE O-P-O-INFP-CAR))
 (684 684 (:TYPE-PRESCRIPTION LEN))
 (570 114 (:DEFINITION LEN))
 (510 510 (:TYPE-PRESCRIPTION A-NATP))
 (482 482 (:TYPE-PRESCRIPTION O-P))
 (418 76 (:DEFINITION NFIX))
 (400 286 (:REWRITE DEFAULT-<-2))
 (336 42 (:DEFINITION KEYS))
 (324 324 (:META CANCEL_PLUS-LESSP-CORRECT))
 (324 286 (:REWRITE DEFAULT-<-1))
 (300 20 (:DEFINITION IS-KEYS-OF-ALIST))
 (284 284 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (284 284 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (280 20 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (266 152 (:REWRITE DEFAULT-+-2))
 (241 241 (:REWRITE O-P-DEF-O-FINP-1))
 (229 229 (:REWRITE NATP-RW))
 (209 19 (:DEFINITION ASSOC-EQUAL))
 (204 204 (:REWRITE A-VALID-NODES-IMPLIES-A-NATP))
 (204 51 (:REWRITE MARKSI-UPDATE-MARKSI))
 (190 38 (:REWRITE ZP-OPEN))
 (190 19 (:DEFINITION TRUE-LISTP-VALUES))
 (152 152 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (152 152 (:REWRITE DEFAULT-+-1))
 (152 38 (:REWRITE <-+-NEGATIVE-0-1))
 (140 20 (:DEFINITION ALISTP))
 (114 114 (:TYPE-PRESCRIPTION NFIX))
 (114 114 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (95 38 (:DEFINITION TRUE-LISTP))
 (80 80 (:REWRITE FIND-2NODE-IN-NEIGHBORS-IF-NEIGHBORS-IS-MARKED-2))
 (51 51 (:REWRITE A-NATP-ST-FILTER-NEIGHBORS-FOR-DEST))
 (38 38 (:TYPE-PRESCRIPTION A-VALID-NODES))
 (30 30 (:REWRITE SUBSETP-TRANS))
 (20 20 (:REWRITE NODUPS-KEYS-NEIGHBORS->DESTSI))
 (19 19 (:TYPE-PRESCRIPTION TRUE-LISTP-VALUES))
 (19 19 (:TYPE-PRESCRIPTION A-VALID-NODES-VALUES))
 (4 2 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (2 2 (:TYPE-PRESCRIPTION CONSP-APPEND . 2))
 (2 2 (:TYPE-PRESCRIPTION CONSP-APPEND . 1))
 (2 2 (:TYPE-PRESCRIPTION BINARY-APPEND))
 )
(UPDATE-MARKSI-2-APPEND-ESCS-PRESERVES-INVARIANT-ESCS2
 (7544 86 (:DEFINITION MARKSI))
 (6281 80 (:DEFINITION A-VALID-NODES))
 (6035 4529 (:REWRITE DEFAULT-CDR))
 (5400 72 (:DEFINITION NODESI))
 (5330 3131 (:REWRITE DEFAULT-<-2))
 (5284 2968 (:REWRITE DEFAULT-+-2))
 (3857 2170 (:REWRITE DEFAULT-CAR))
 (3748 3556 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3498 44 (:DEFINITION A-VALID-NODES-VALUES))
 (3464 3131 (:REWRITE DEFAULT-<-1))
 (2968 2968 (:REWRITE DEFAULT-+-1))
 (2812 2812 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (2792 670 (:REWRITE O-P-O-INFP-CAR))
 (2475 83 (:REWRITE CONSP-NEIGHBORSI->NEIGHBORSI))
 (2196 2196 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (1832 200 (:REWRITE FIND-2NODE-UPDATE-MARKSI-2))
 (1517 36 (:DEFINITION IS-KEYS-OF-ALIST))
 (1318 294 (:REWRITE ZP-OPEN))
 (1245 1245 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (1176 112 (:DEFINITION A-NATP))
 (782 670 (:REWRITE O-P-DEF-O-FINP-1))
 (644 72 (:DEFINITION KEYS))
 (592 592 (:TYPE-PRESCRIPTION A-NATP))
 (560 560 (:TYPE-PRESCRIPTION UPDATE-MARKSI))
 (504 36 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (426 426 (:TYPE-PRESCRIPTION ST-FILTER-NEIGHBORS-FOR-DEST))
 (414 414 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (414 414 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (396 396 (:REWRITE MEMBER-SUBSETP))
 (394 36 (:DEFINITION TRUE-LISTP-VALUES))
 (314 314 (:REWRITE CONSP-ESCI-->ESCI))
 (304 16 (:REWRITE NTH-ADD1))
 (298 298 (:REWRITE NATP-RW))
 (238 30 (:DEFINITION ALISTP))
 (228 76 (:REWRITE FOLD-CONSTS-IN-+))
 (224 224 (:REWRITE A-VALID-NODES-IMPLIES-A-NATP))
 (224 56 (:REWRITE MARKSI-UPDATE-MARKSI))
 (224 56 (:REWRITE <-0-+-NEGATIVE-1))
 (168 84 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (153 72 (:DEFINITION TRUE-LISTP))
 (112 112 (:REWRITE FIND-2NODE-IN-NEIGHBORS-IF-NEIGHBORS-IS-MARKED-2))
 (84 84 (:TYPE-PRESCRIPTION CONSP-APPEND . 2))
 (84 84 (:TYPE-PRESCRIPTION CONSP-APPEND . 1))
 (84 84 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (72 72 (:TYPE-PRESCRIPTION KEYS))
 (56 56 (:REWRITE A-NATP-ST-FILTER-NEIGHBORS-FOR-DEST))
 (30 30 (:TYPE-PRESCRIPTION ALISTP))
 (28 2 (:DEFINITION SUBSETP-EQUAL))
 (24 24 (:REWRITE EQUAL-CONSTANT-+))
 (20 20 (:REWRITE CDR-CONS))
 (9 9 (:REWRITE TRUE-LISTP-NEIGHBORSI))
 (9 9 (:REWRITE A-VALID-NODES-NEIGHBORSI))
 (8 4 (:REWRITE POSP-NATP))
 (6 6 (:REWRITE SUBSETP-TRANS))
 (6 6 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (6 6 (:REWRITE NTH-0-CONS))
 )
(STEP1-PRESERVES-INVARIANT-ESCS2-INDUCTIVE
 (693661 306 (:DEFINITION E-013-MARKED-E-D-PATH))
 (286950 918 (:DEFINITION ST-FIND-D-PATH))
 (250260 918 (:DEFINITION ST-FIND-NEXT-D-STEP))
 (121312 3826 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
 (111758 1008 (:DEFINITION SHOW-NODESET))
 (101926 1157 (:REWRITE ALGO-PRESERVES-4MARKING))
 (101926 1157 (:REWRITE ALGO-PRESERVES-3MARKING))
 (101926 1157 (:REWRITE ALGO-PRESERVES-2MARKING))
 (98838 75070 (:REWRITE DEFAULT-CAR))
 (89443 46805 (:REWRITE DEFAULT-+-2))
 (84995 66481 (:REWRITE DEFAULT-CDR))
 (80152 50190 (:REWRITE DEFAULT-<-2))
 (67249 50190 (:REWRITE DEFAULT-<-1))
 (59142 59142 (:META CANCEL_PLUS-LESSP-CORRECT))
 (46932 46805 (:REWRITE DEFAULT-+-1))
 (39136 9784 (:REWRITE O-P-O-INFP-CAR))
 (29442 1836 (:DEFINITION REV))
 (28233 677 (:DEFINITION ST-FILTER-UNMARKED123-NODES))
 (24010 24010 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (24010 24010 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (22813 160 (:DEFINITION A-DESTS-E-2NEIGHBOR))
 (21910 21910 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (16446 378 (:REWRITE MEMBER-ST-FILTER-UNMARKED123-NODES))
 (15147 3679 (:DEFINITION BINARY-APPEND))
 (14304 165 (:DEFINITION FIND-2NODE))
 (13121 316 (:REWRITE ST-FILTER-UNMARKED123-NODES-UPDATE-MARKSI-UNMARKED))
 (13078 419 (:REWRITE REMOVE-EQUAL-NON-MEMBER-EQUAL))
 (9784 9784 (:REWRITE O-P-DEF-O-FINP-1))
 (9061 342 (:REWRITE MEMBER-SHOW-ALL-NODES))
 (8634 8634 (:REWRITE NATP-RW))
 (7672 85 (:DEFINITION A-VALID-NODES-VALUES))
 (7572 121 (:REWRITE EQUAL-OCCURRENCES-EQUAL-ONE))
 (7081 7081 (:TYPE-PRESCRIPTION ST-FILTER-NEIGHBORS-FOR-DEST))
 (6328 1582 (:REWRITE FOLD-CONSTS-IN-+))
 (6309 6309 (:REWRITE EQUAL-CONSTANT-+))
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 (4722 121 (:REWRITE EQUAL-OCCURRENCES-EQUAL-ZERO))
 (4620 110 (:DEFINITION IS-KEYS-OF-ALIST))
 (4162 224 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (3672 3672 (:TYPE-PRESCRIPTION ST-FIND-NEXT-D-STEP))
 (3672 3672 (:REWRITE CDR-CONS))
 (3672 3672 (:REWRITE CAR-CONS))
 (2586 45 (:REWRITE MEMBER-SHOW-NODESET))
 (2534 6 (:REWRITE FIND-2NODE-UPDATE-MARKSI-4))
 (1836 1836 (:TYPE-PRESCRIPTION REV))
 (1836 306 (:REWRITE O-INFP->NEQ-0))
 (1760 220 (:DEFINITION KEYS))
 (1467 1467 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1451 14 (:REWRITE A-DESTS-E-2NEIGHBOR-UPDATE-MARKSI-2-PRESERVED))
 (1416 484 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (1288 6 (:REWRITE A-DESTS-E-2NEIGHBOR-UPDATE-MARKSI-4))
 (918 918 (:TYPE-PRESCRIPTION O-FINP))
 (918 306 (:REWRITE O-FIRST-EXPT-O-INFP))
 (850 85 (:DEFINITION TRUE-LISTP-VALUES))
 (824 2 (:REWRITE FIND-2NODE-UPDATE-MARKSI-3))
 (770 110 (:DEFINITION ALISTP))
 (726 726 (:TYPE-PRESCRIPTION NATURALP-OCCURRENCES-EQUAL))
 (704 160 (:REWRITE A-NATP-NEIGHBORS))
 (612 306 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (425 170 (:DEFINITION TRUE-LISTP))
 (419 2 (:REWRITE A-DESTS-E-2NEIGHBOR-UPDATE-MARKSI-3))
 (418 4 (:LINEAR ALGO-DOES-NOT-INCREASE-NUMBER-OF-UNMARKED-NODES))
 (369 18 (:REWRITE A-DESTS-E-2NEIGHBOR-UPDATE-MARKSI-1))
 (366 186 (:REWRITE ST-FILTER-UNMARKED-123-NODES-UPDATE-MARKSI))
 (242 121 (:REWRITE DEFAULT-UNARY-MINUS))
 (229 151 (:REWRITE ST-FILTER-UNMARKED123-NODES-UPDATE-MARKSI-1))
 (220 220 (:TYPE-PRESCRIPTION KEYS))
 (210 14 (:REWRITE FIND-2NODE-UPDATE-MARKSI-2))
 (172 44 (:REWRITE MARKSI-APPEND-TO-DEP))
 (110 110 (:REWRITE NODUPS-KEYS-NEIGHBORS->DESTSI))
 (110 110 (:REWRITE NEIGHBORS-ARE-KEYS-OF-NEIGHBORS->DESTSI))
 (103 7 (:REWRITE REWRITE-ESCI-APPEND-TO-ESC-UNCONDITIONAL))
 (100 50 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (85 85 (:TYPE-PRESCRIPTION TRUE-LISTP-VALUES))
 (85 85 (:TYPE-PRESCRIPTION A-VALID-NODES-VALUES))
 (72 18 (:LINEAR LEN-ST-FILTER-UNMARKED-123-NODES-UPDATE-MARKSI-4))
 (61 12 (:REWRITE FIND-2NODE-UPDATE-MARKSI-1))
 (50 50 (:TYPE-PRESCRIPTION CONSP-APPEND . 2))
 (50 50 (:TYPE-PRESCRIPTION CONSP-APPEND . 1))
 (50 50 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (30 12 (:REWRITE ST-FILTER-UNMARKED123-NODES-UPDATE-MARKSI-2))
 (28 7 (:REWRITE FIND-2NODE-IN-NEIGHBORS-IF-NEIGHBORS-IS-MARKED-2))
 (24 6 (:REWRITE ST-FILTER-UNMARKED123-NODES-UPDATE-MARKSI-3))
 (8 2 (:LINEAR LEN-ST-FILTER-UNMARKED-123-NODES-UPDATE-MARKSI-3))
 (8 2 (:LINEAR LEN-ST-FILTER-UNMARKED-123-NODES-UPDATE-MARKSI-2))
 (7 7 (:REWRITE A-NATP-ST-FILTER-NEIGHBORS-FOR-DEST))
 )
(UPDATE-MARKSI-2-PRESERVES-A-DESTS-E-2NEIGHBOR
 (1617 75 (:REWRITE NTH-WITH-LARGE-INDEX))
 (1278 6 (:DEFINITION VALID-GRAPH))
 (1050 12 (:DEFINITION A-VALID-NODES))
 (900 12 (:DEFINITION NODESI))
 (576 6 (:DEFINITION A-VALID-NODES-VALUES))
 (450 450 (:TYPE-PRESCRIPTION LEN))
 (445 287 (:REWRITE DEFAULT-CAR))
 (434 300 (:REWRITE DEFAULT-CDR))
 (429 75 (:DEFINITION LEN))
 (425 17 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
 (384 6 (:DEFINITION FILLED-GRAPHP))
 (340 82 (:REWRITE O-P-O-INFP-CAR))
 (275 50 (:DEFINITION NFIX))
 (243 168 (:REWRITE DEFAULT-<-2))
 (193 193 (:META CANCEL_PLUS-LESSP-CORRECT))
 (193 168 (:REWRITE DEFAULT-<-1))
 (192 29 (:DEFINITION MEMBER-EQUAL))
 (175 100 (:REWRITE DEFAULT-+-2))
 (164 164 (:TYPE-PRESCRIPTION O-P))
 (128 13 (:DEFINITION A-NATP))
 (125 25 (:REWRITE ZP-OPEN))
 (100 100 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (100 100 (:REWRITE DEFAULT-+-1))
 (100 25 (:REWRITE <-+-NEGATIVE-0-1))
 (96 12 (:DEFINITION KEYS))
 (94 82 (:REWRITE O-P-DEF-O-FINP-1))
 (90 6 (:DEFINITION IS-KEYS-OF-ALIST))
 (84 6 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (75 75 (:TYPE-PRESCRIPTION NFIX))
 (75 75 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (66 6 (:REWRITE REWRITE-MEMBER-KEYS))
 (60 60 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (60 60 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (60 6 (:DEFINITION TRUE-LISTP-VALUES))
 (58 58 (:REWRITE MEMBER-SUBSETP))
 (52 29 (:TYPE-PRESCRIPTION TRUE-LISTP-MEMBER-EQUAL))
 (48 48 (:REWRITE CONSP-NEIGHBORS<->NEIGHBORS))
 (42 6 (:DEFINITION ALISTP))
 (37 37 (:REWRITE NATP-RW))
 (30 12 (:DEFINITION TRUE-LISTP))
 (26 26 (:REWRITE A-VALID-NODES-IMPLIES-A-NATP))
 (24 6 (:REWRITE MARKSI-UPDATE-MARKSI))
 (23 23 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (23 23 (:TYPE-PRESCRIPTION CONSP-MEMBER-EQUAL))
 (12 12 (:TYPE-PRESCRIPTION KEYS))
 (12 12 (:TYPE-PRESCRIPTION A-VALID-NODES))
 (9 9 (:REWRITE FIND-2NODE-IN-NEIGHBORS-IF-NEIGHBORS-IS-MARKED-2))
 (7 7 (:REWRITE A-NATP-ST-FILTER-NEIGHBORS-FOR-DEST))
 (6 6 (:TYPE-PRESCRIPTION TRUE-LISTP-VALUES))
 (6 6 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (6 6 (:TYPE-PRESCRIPTION ALISTP))
 (6 6 (:TYPE-PRESCRIPTION A-VALID-NODES-VALUES))
 (6 6 (:REWRITE TRUE-LISTP-VALUES-NEIGHBORS->DESTSI))
 (6 6 (:REWRITE TRUE-LISTP-NEIGHBORS))
 (6 6 (:REWRITE NODUPS-KEYS-NEIGHBORS->DESTSI))
 (6 6 (:REWRITE A-VALID-NODES-VALUES-NEIGHBORS->DESTSI))
 (6 6 (:REWRITE A-VALID-NODES-NEIGHBORS))
 )
(UPDATE-MARKSI-2-PRESERVES-INVARIANT-ESCS2
 (8899 488 (:REWRITE NTH-WITH-LARGE-INDEX))
 (2501 484 (:DEFINITION LEN))
 (1659 16 (:DEFINITION FIND-2NODE))
 (1392 16 (:DEFINITION A-VALID-NODES))
 (1378 16 (:DEFINITION MARKSI))
 (1200 16 (:DEFINITION NODESI))
 (1178 691 (:REWRITE DEFAULT-<-2))
 (1127 617 (:REWRITE DEFAULT-+-2))
 (1086 949 (:REWRITE DEFAULT-CDR))
 (812 812 (:META CANCEL_PLUS-LESSP-CORRECT))
 (787 127 (:DEFINITION NFIX))
 (781 691 (:REWRITE DEFAULT-<-1))
 (776 8 (:DEFINITION A-VALID-NODES-VALUES))
 (617 617 (:REWRITE DEFAULT-+-1))
 (564 395 (:REWRITE DEFAULT-CAR))
 (518 518 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (478 478 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (416 16 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
 (406 97 (:REWRITE O-P-O-INFP-CAR))
 (380 95 (:REWRITE <-+-NEGATIVE-0-1))
 (377 67 (:REWRITE ZP-OPEN))
 (270 18 (:REWRITE FIND-2NODE-UPDATE-MARKSI-2))
 (194 194 (:TYPE-PRESCRIPTION O-P))
 (192 32 (:DEFINITION MEMBER-EQUAL))
 (189 18 (:DEFINITION A-NATP))
 (144 16 (:DEFINITION KEYS))
 (115 97 (:REWRITE O-P-DEF-O-FINP-1))
 (112 8 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (112 8 (:DEFINITION IS-KEYS-OF-ALIST))
 (104 26 (:REWRITE <-0-+-NEGATIVE-1))
 (96 32 (:REWRITE FOLD-CONSTS-IN-+))
 (90 90 (:TYPE-PRESCRIPTION UPDATE-MARKSI))
 (90 90 (:TYPE-PRESCRIPTION A-NATP))
 (88 8 (:DEFINITION TRUE-LISTP-VALUES))
 (87 87 (:REWRITE CONSP-ESCI-->ESCI))
 (75 75 (:TYPE-PRESCRIPTION ST-FILTER-NEIGHBORS-FOR-DEST))
 (72 72 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (72 72 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (64 64 (:REWRITE MEMBER-SUBSETP))
 (56 32 (:TYPE-PRESCRIPTION TRUE-LISTP-MEMBER-EQUAL))
 (56 7 (:DEFINITION ALISTP))
 (43 43 (:REWRITE NATP-RW))
 (36 36 (:TYPE-PRESCRIPTION NATP))
 (36 36 (:REWRITE A-VALID-NODES-IMPLIES-A-NATP))
 (36 9 (:REWRITE MARKSI-UPDATE-MARKSI))
 (32 16 (:DEFINITION TRUE-LISTP))
 (24 24 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (18 18 (:REWRITE UPDATE-MARKSI-2-PRESERVES-A-DESTS-E-2NEIGHBOR))
 (16 16 (:TYPE-PRESCRIPTION KEYS))
 (9 9 (:REWRITE FIND-2NODE-IN-NEIGHBORS-IF-NEIGHBORS-IS-MARKED-2))
 (9 9 (:REWRITE A-NATP-ST-FILTER-NEIGHBORS-FOR-DEST))
 (7 7 (:TYPE-PRESCRIPTION ALISTP))
 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(STEP1-PRESERVES-INVARIANT-ESCS2
 (25960 23 (:DEFINITION E-D-E-D-PATH-TO-013-MARKED-NODE))
 (25569 23 (:DEFINITION E-013-MARKED-E-D-PATH))
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 (12606 69 (:DEFINITION ST-FIND-NEXT-D-STEP))
 (9567 590 (:DEFINITION MEMBER-EQUAL))
 (8982 282 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
 (5091 3767 (:REWRITE DEFAULT-CAR))
 (4122 2097 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (4070 2586 (:REWRITE DEFAULT-CDR))
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 (2592 630 (:REWRITE O-P-O-INFP-CAR))
 (2346 54 (:REWRITE REMOVE-EQUAL-NON-MEMBER-EQUAL))
 (2332 1175 (:REWRITE DEFAULT-+-2))
 (2057 848 (:TYPE-PRESCRIPTION TRUE-LISTP-MEMBER-EQUAL))
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 (1798 1798 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1798 1798 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (1770 69 (:REWRITE ALGO-PRESERVES-3MARKING))
 (1770 69 (:REWRITE ALGO-PRESERVES-2MARKING))
 (1500 54 (:REWRITE MEMBER-ST-FILTER-UNMARKED123-NODES))
 (1338 18 (:REWRITE MEMBER-SHOW-NODESET))
 (1187 1175 (:REWRITE DEFAULT-+-1))
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 (1020 18 (:REWRITE LEN-REMOVE-EQUAL))
 (936 36 (:REWRITE NTH-WITH-LARGE-INDEX))
 (840 40 (:DEFINITION ST-FILTER-UNMARKED123-NODES))
 (720 5 (:DEFINITION FILLED-GRAPHP))
 (702 630 (:REWRITE O-P-DEF-O-FINP-1))
 (684 18 (:DEFINITION NTH))
 (666 18 (:DEFINITION REMOVE-EQUAL))
 (630 520 (:REWRITE DEFAULT-<-1))
 (568 76 (:DEFINITION LEN))
 (548 548 (:TYPE-PRESCRIPTION TRUE-LISTP-ST-FILTER-UNMARKED123-NODES))
 (538 538 (:META CANCEL_PLUS-LESSP-CORRECT))
 (525 525 (:REWRITE EQUAL-CONSTANT-+))
 (440 5 (:DEFINITION VALID-GRAPH))
 (403 403 (:REWRITE NATP-RW))
 (378 18 (:REWRITE EQUAL-OCCURRENCES-EQUAL-ZERO))
 (378 18 (:REWRITE EQUAL-OCCURRENCES-EQUAL-ONE))
 (357 357 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (357 357 (:TYPE-PRESCRIPTION CONSP-MEMBER-EQUAL))
 (336 24 (:DEFINITION SUBSETP-EQUAL))
 (288 6 (:DEFINITION INVARIANT-ESCS2))
 (276 276 (:TYPE-PRESCRIPTION ST-FIND-NEXT-D-STEP))
 (216 6 (:DEFINITION A-DESTS-E-2NEIGHBOR))
 (215 5 (:REWRITE REWRITE-MEMBER-KEYS))
 (210 5 (:DEFINITION IS-KEYS-OF-ALIST))
 (198 36 (:DEFINITION NFIX))
 (192 72 (:TYPE-PRESCRIPTION |x < y  =>  0 < y-x|))
 (150 150 (:TYPE-PRESCRIPTION ST-FILTER-NEIGHBORS-FOR-DEST))
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 (120 5 (:DEFINITION A-VALID-NODES-VALUES))
 (108 108 (:TYPE-PRESCRIPTION NATURALP-OCCURRENCES-EQUAL))
 (80 10 (:DEFINITION KEYS))
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 (72 18 (:REWRITE <-+-NEGATIVE-0-1))
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 (54 18 (:REWRITE MEMBER-SHOW-ALL-NODES))
 (51 51 (:REWRITE SUBSETP-TRANS))
 (50 5 (:DEFINITION TRUE-LISTP-VALUES))
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 (46 23 (:REWRITE O-FIRST-EXPT-DEF-O-FINP))
 (36 36 (:TYPE-PRESCRIPTION NFIX))
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 (36 18 (:REWRITE DEFAULT-UNARY-MINUS))
 (36 18 (:REWRITE A-NATP-NEIGHBORS))
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 (5 5 (:TYPE-PRESCRIPTION IS-KEYS-OF-ALIST))
 (5 5 (:TYPE-PRESCRIPTION ALISTP))
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 (5 5 (:REWRITE TRUE-LISTP-NEIGHBORS))
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 (5 5 (:REWRITE NEIGHBORS-ARE-KEYS-OF-NEIGHBORS->DESTSI))
 (5 5 (:REWRITE A-VALID-NODES-VALUES-NEIGHBORS->DESTSI))
 (3 3 (:TYPE-PRESCRIPTION ST-ESCAPABLE-INV))
 )
(FIND-2NODE-UPDATE-ESCI
 (167 104 (:REWRITE DEFAULT-<-2))
 (138 80 (:REWRITE DEFAULT-+-2))
 (116 116 (:META CANCEL_PLUS-LESSP-CORRECT))
 (116 104 (:REWRITE DEFAULT-<-1))
 (115 115 (:REWRITE DEFAULT-CDR))
 (93 9 (:REWRITE LEN-UPDATE-NTH1))
 (88 20 (:DEFINITION UPDATE-NTH))
 (80 80 (:REWRITE DEFAULT-+-1))
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 (48 48 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
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 (48 12 (:REWRITE <-+-NEGATIVE-0-1))
 (32 8 (:REWRITE O-P-O-INFP-CAR))
 (16 16 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (16 16 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (8 8 (:REWRITE O-P-DEF-O-FINP-1))
 )
(A-DESTS-E-2NEIGHBOR-UPDATE-ESCI
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 (420 420 (:TYPE-PRESCRIPTION LEN))
 (350 70 (:DEFINITION LEN))
 (260 10 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
 (220 40 (:DEFINITION NFIX))
 (194 154 (:REWRITE DEFAULT-CDR))
 (190 120 (:REWRITE DEFAULT-<-2))
 (160 90 (:REWRITE DEFAULT-+-2))
 (140 140 (:META CANCEL_PLUS-LESSP-CORRECT))
 (140 120 (:REWRITE DEFAULT-<-1))
 (140 100 (:REWRITE DEFAULT-CAR))
 (90 90 (:REWRITE DEFAULT-+-1))
 (80 80 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (80 20 (:REWRITE O-P-O-INFP-CAR))
 (80 20 (:REWRITE <-+-NEGATIVE-0-1))
 (70 70 (:TYPE-PRESCRIPTION NFIX))
 (70 70 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (60 20 (:REWRITE ZP-OPEN))
 (60 10 (:DEFINITION MEMBER-EQUAL))
 (23 23 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (23 23 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (20 20 (:REWRITE O-P-DEF-O-FINP-1))
 (20 20 (:REWRITE MEMBER-SUBSETP))
 (20 10 (:TYPE-PRESCRIPTION TRUE-LISTP-MEMBER-EQUAL))
 (10 10 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (10 10 (:TYPE-PRESCRIPTION CONSP-MEMBER-EQUAL))
 (10 10 (:REWRITE CONSP-ESCI-->ESCI))
 )
(FIND-2NODE-IN-NEIGHBORS
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 (1364 66 (:REWRITE NTH-WITH-LARGE-INDEX))
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 (777 777 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (592 407 (:REWRITE DEFAULT-CDR))
 (495 126 (:REWRITE O-P-O-INFP-CAR))
 (396 396 (:TYPE-PRESCRIPTION LEN))
 (330 66 (:DEFINITION LEN))
 (242 44 (:DEFINITION NFIX))
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 (210 14 (:DEFINITION IS-KEYS-OF-ALIST))
 (196 14 (:DEFINITION NO-DUPLICATESP-EQUAL))
 (190 190 (:META CANCEL_PLUS-LESSP-CORRECT))
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 (154 88 (:REWRITE DEFAULT-+-2))
 (143 143 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (143 143 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (123 123 (:REWRITE O-P-DEF-O-FINP-1))
 (110 22 (:REWRITE ZP-OPEN))
 (110 11 (:DEFINITION TRUE-LISTP-VALUES))
 (106 106 (:REWRITE CONSP-NEIGHBORS<->NEIGHBORS))
 (88 88 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
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 (84 12 (:DEFINITION ALISTP))
 (66 66 (:TYPE-PRESCRIPTION NFIX))
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 (55 22 (:DEFINITION TRUE-LISTP))
 (47 47 (:REWRITE NATP-RW))
 (22 22 (:TYPE-PRESCRIPTION A-VALID-NODES))
 (14 14 (:REWRITE SUBSETP-TRANS))
 (14 14 (:REWRITE NEIGHBORS-ARE-KEYS-OF-NEIGHBORS->DESTSI))
 (11 11 (:TYPE-PRESCRIPTION TRUE-LISTP-VALUES))
 (11 11 (:TYPE-PRESCRIPTION A-VALID-NODES-VALUES))
 (4 4 (:REWRITE A-VALID-NODES-IMPLIES-A-NATP))
 (2 2 (:REWRITE REWRITE-A-NATP-KEYS))
 )
(2MARKED-NEIGHBOR-IMPLIES-A-DESTS-E-2NEIGHBOR
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 (900 12 (:DEFINITION NODESI))
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 (327 230 (:REWRITE DEFAULT-CDR))
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 (216 216 (:TYPE-PRESCRIPTION LEN))
 (180 36 (:DEFINITION LEN))
 (175 7 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
 (132 24 (:DEFINITION NFIX))
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 (127 91 (:REWRITE DEFAULT-<-2))
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 (103 103 (:META CANCEL_PLUS-LESSP-CORRECT))
 (103 91 (:REWRITE DEFAULT-<-1))
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 (7 7 (:REWRITE FIND-2NODE-IN-NEIGHBORS))
 (6 6 (:TYPE-PRESCRIPTION TRUE-LISTP-VALUES))
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(A-DESTS-E-2NEIGHBOR-HOLDS-FOR-ALL-DESTS-LEADING-TO-2NEIGHBORS
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 (970 10 (:DEFINITION A-VALID-NODES-VALUES))
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 (751 424 (:REWRITE DEFAULT-<-2))
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 (327 327 (:TYPE-PRESCRIPTION NFIX))
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 )
(TEMP24.0
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(APPEND-ESCS-LEADING-TO-2NEIGHBORS-PRESERVE-INVARIANT-ESCS2-SETMINUS
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 (495 27 (:DEFINITION IS-KEYS-OF-ALIST))
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(APPEND-ESCS-LEADING-TO-2NEIGHBORS-PRESERVE-INVARIANT-ESCS2
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 (299 22 (:DEFINITION ST-FILTER-2MARKED-NODES))
 (264 22 (:DEFINITION ASSOC-EQUAL))
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 (257 257 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (255 255 (:REWRITE O-P-DEF-O-FINP-1))
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 )
(TEMP19.0
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 (6 3 (:REWRITE DEFAULT-<-2))
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 (3 3 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3 3 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
 )
(STEP2-PRESERVES-INVARIANT-ESCS2
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(ALGO-PRESERVES-INVARIANT-ESCS2
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(SPEC-OF-INVARIANT-ESCS2
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 (234 198 (:REWRITE DEFAULT-CDR))
 (234 9 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
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 (217 178 (:REWRITE DEFAULT-<-1))
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 (156 39 (:REWRITE <-+-NEGATIVE-0-1))
 (147 27 (:REWRITE ZP-OPEN))
 (135 99 (:REWRITE DEFAULT-CAR))
 (99 99 (:LINEAR LEQ-POSITION-EQUAL-LEN))
 (72 18 (:REWRITE O-P-O-INFP-CAR))
 (54 9 (:DEFINITION MEMBER-EQUAL))
 (48 12 (:REWRITE <-0-+-NEGATIVE-1))
 (36 36 (:TYPE-PRESCRIPTION O-P))
 (27 27 (:TYPE-PRESCRIPTION ST-FILTER-NEIGHBORS-FOR-DEST))
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(A-CLEAR-IMPLIES-INVARIANT-ESCS2
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 (222 222 (:REWRITE DEFAULT-+-1))
 (130 5 (:DEFINITION ST-FILTER-NEIGHBORS-FOR-DEST))
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 (40 10 (:REWRITE O-P-O-INFP-CAR))
 (30 5 (:REWRITE O-INFP->NEQ-0))
 (30 5 (:DEFINITION MEMBER-EQUAL))
 (15 15 (:TYPE-PRESCRIPTION ST-FILTER-NEIGHBORS-FOR-DEST))
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 (15 15 (:REWRITE 2MARKED-NEIGHBOR-IMPLIES-A-DESTS-E-2NEIGHBOR))
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 (5 5 (:TYPE-PRESCRIPTION TRUE-LISTP))
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(APPEND-TO-ESC-PRESERVES-INVARIANT-COMP
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(UPDATE-MARKSI-2-PRESERVES-INVARIANT-COMP
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 (20 20 (:REWRITE CONSP-NEIGHBORSI->NEIGHBORSI))
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(SUBSETP-DEPI-AFTER-STEP1
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(MEMBER-VALID-NODES->NODESI=1
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 (50 50 (:LINEAR LEQ-POSITION-EQUAL-LEN))
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(DEPI-APPEND-TO-DEP-UPDATE-MARKSI
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 (266 266 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
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(DEPI-APPEND-TO-ESC-UPDATE-MARKSI
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(SUBSETP-ESCI-AFTER-STEP1
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(STEP1-PUTS-DEST-TO-NEIGHBOR-IN-ESC-OR-DEP
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(TEMP1.16
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(TEMP2.0
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(SPEC-OF-INVARIANT-COMP2
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(TEMP1.15
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(UPDATE-MARKSI-2-PRESERVES-INVARIANT-COMP-SINK
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(UPDATE-MARKSI-2-PRESERVES-INVARIANT-COMP-ALREADY-2
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(UPDATE-MARKSI-3-PRESERVES-INVARIANT-COMP-VISITED
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(UPDATE-MARKSI-4-PRESERVES-INVARIANT-COMP-VISITED
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(STEP1-PRESERVES-INVARIANT-COMP-INDUCTIVE
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 )
(STEP1-PRESERVES-INVARIANT-COMP
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 )
(ALGO-PRESERVES-INVARIANT-COMP
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 )
(SPEC-OF-INVARIANT-COMP4
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 (54 54 (:REWRITE CONSP-ASSOC-NEIGHBORS->DESTSI-->ASSOC-NEIGHBORS->DESTSI))
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 )
(SPEC-OF-INVARIANT-COMP
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 (54 54 (:REWRITE CONSP-ASSOC-NEIGHBORS->DESTSI-->ASSOC-NEIGHBORS->DESTSI))
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 )
(A-CLEAR-IMPLIES-INVARIANT-COMP
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 )
