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(BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1
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(BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2
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 (23 22 (:REWRITE DEFAULT-<-1))
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 (21 21 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (14 14 (:REWRITE NATP-RW))
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 (7 7 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (6 6 (:REWRITE DEFAULT-+-1))
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(TERM-GRAPH-P-MAIN-PROPERTY)
(NEIGHBORS
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 (28 4 (:DEFINITION NTH))
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 (14 14 (:REWRITE DEFAULT-CAR))
 (12 1 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (10 2 (:DEFINITION LEN))
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 (6 6 (:REWRITE DEFAULT-+-1))
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 (4 4 (:REWRITE ZP-OPEN))
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 (2 1 (:DEFINITION TRUE-LISTP))
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 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(NEIGHBORS-BOUNDED-NAT-TRUE-LISTP
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 (157 77 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
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 (116 116 (:REWRITE DEFAULT-CDR))
 (90 90 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
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 (52 52 (:REWRITE DEFAULT-+-1))
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 (32 32 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (27 27 (:REWRITE ZP-OPEN))
 (22 22 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (22 22 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(NFIX-NATP)
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 (22 22 (:REWRITE DEFAULT-CAR))
 (14 14 (:REWRITE DEFAULT-CDR))
 (11 11 (:META CANCEL_TIMES-EQUAL-CORRECT))
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 (3 3 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
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 (2 2 (:REWRITE DEFAULT-+-1))
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(NFIX-NTH
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 (6 6 (:REWRITE DEFAULT-CAR))
 (6 2 (:REWRITE ZP-OPEN))
 (4 3 (:REWRITE DEFAULT-<-1))
 (3 3 (:REWRITE DEFAULT-<-2))
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 (2 2 (:REWRITE DEFAULT-CDR))
 (2 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE DEFAULT-+-1))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(MAP-NFIX)
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 (19 19 (:REWRITE DEFAULT-CDR))
 (17 17 (:REWRITE DEFAULT-<-2))
 (17 17 (:REWRITE DEFAULT-<-1))
 (17 17 (:META CANCEL_PLUS-LESSP-CORRECT))
 (15 15 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (15 15 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(BOUNDED-NATP)
(COUNT-BOUNDED-NATP-NOT-IN
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(MEASURE-DAG-P)
(MEASURE-DAG-P-ORDINALP
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 (17 9 (:REWRITE DEFAULT-CAR))
 (15 3 (:DEFINITION LEN))
 (13 8 (:REWRITE DEFAULT-+-2))
 (10 7 (:REWRITE DEFAULT-CDR))
 (9 1 (:REWRITE ZP-OPEN))
 (8 8 (:REWRITE DEFAULT-+-1))
 (8 1 (:DEFINITION MEMBER-EQUAL))
 (3 1 (:DEFINITION NOT))
 (2 2 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (2 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (1 1 (:REWRITE EQUAL-CONSTANT-+))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(NATP-LEN)
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 (6 3 (:REWRITE DEFAULT-+-2))
 (4 4 (:REWRITE DEFAULT-<-1))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (3 3 (:REWRITE DEFAULT-CDR))
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(NTH-NON-NIL
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 (4 4 (:REWRITE ZP-OPEN))
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(COUNT-BOUNDED-NATP-NOT-IN-CONS-1
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 (35 35 (:REWRITE DEFAULT-+-1))
 (18 8 (:REWRITE DEFAULT-<-1))
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 (17 17 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(COUNT-BOUNDED-NATP-NOT-IN-CONS-2
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 (105 105 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (91 91 (:REWRITE DEFAULT-CDR))
 (91 91 (:REWRITE DEFAULT-CAR))
 (90 30 (:REWRITE FOLD-CONSTS-IN-+))
 (76 76 (:REWRITE EQUAL-CONSTANT-+))
 (35 21 (:REWRITE ZP-OPEN))
 (25 20 (:REWRITE DEFAULT-<-2))
 (22 22 (:META CANCEL_PLUS-LESSP-CORRECT))
 (20 20 (:REWRITE NATP-RW))
 (20 20 (:REWRITE DEFAULT-<-1))
 (8 2 (:REWRITE <-0-+-NEGATIVE-1))
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(MEASURE-DAG-P-RECURSION-1
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 (537 289 (:REWRITE DEFAULT-+-2))
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 (225 137 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (196 178 (:REWRITE DEFAULT-CDR))
 (150 126 (:REWRITE DEFAULT-CAR))
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 (111 111 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (29 17 (:REWRITE DEFAULT-<-2))
 (25 17 (:REWRITE DEFAULT-<-1))
 (4 4 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
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(MEASURE-DAG-P-RECURSION-2
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(LIST-OF-N
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 (4 4 (:REWRITE ZP-OPEN))
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 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(DAG-P
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 (11 11 (:REWRITE DEFAULT-CDR))
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 (4 2 (:REWRITE DEFAULT-<-2))
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 (2 1 (:DEFINITION TRUE-LISTP))
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 (1 1 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(REL-GRAPH)
(PATH-P)
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 (997 907 (:REWRITE DEFAULT-CAR))
 (835 167 (:DEFINITION MAP-NFIX))
 (368 296 (:REWRITE NATP-RW))
 (334 334 (:TYPE-PRESCRIPTION NEIGHBORS))
 (167 167 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (167 167 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(CYCLE-P)
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 (8 8 (:REWRITE DEFAULT-CAR))
 (3 3 (:REWRITE DEFAULT-CDR))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(ONE-CYCLIC-PATH)
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 (1907 1256 (:REWRITE DEFAULT-CDR))
 (555 111 (:DEFINITION MAP-NFIX))
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 (48 6 (:DEFINITION LAST))
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 (27 27 (:META CANCEL_TIMES-EQUAL-CORRECT))
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(MEMBER-CAR-CDR-NO-DUPLICATESP
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(NO-DUPLICATESP-APPEND-CONS
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 (187 23 (:DEFINITION MEMBER-EQUAL))
 (61 49 (:REWRITE DEFAULT-CDR))
 (56 44 (:REWRITE DEFAULT-CAR))
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 (24 24 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(CYCLIC-PATH-AUX-PATH-P-NO-DUPLICATESP
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 (234 150 (:REWRITE DEFAULT-CAR))
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 (54 54 (:REWRITE CONSP-REVLIST))
 (24 24 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (24 24 (:META CANCEL_PLUS-EQUAL-CORRECT))
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(DAG-P-SOUNDNESS
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 (18 18 (:REWRITE DEFAULT-CAR))
 (12 12 (:REWRITE DEFAULT-CDR))
 (12 6 (:REWRITE DEFAULT-+-2))
 (10 10 (:TYPE-PRESCRIPTION NFIX))
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 (2 2 (:TYPE-PRESCRIPTION NEIGHBORS))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (1 1 (:REWRITE CDR-CONS))
 (1 1 (:REWRITE CAR-CONS))
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(EXTENSION-TO-CYCLIC-PATH)
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 (24 10 (:REWRITE DEFAULT-CDR))
 (8 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (8 1 (:REWRITE DEFAULT-<-2))
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 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
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 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
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(DAG-P-AUX-COMPLETENESS-MAIN-LEMMA
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 (132 132 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (24 12 (:DEFINITION TRUE-LISTP))
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 (2 2 (:REWRITE DEFAULT-<-2))
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(MAKE-SIMPLE-CYCLE-AUX)
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 (35 35 (:REWRITE DEFAULT-CDR))
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 (24 24 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (23 23 (:REWRITE DEFAULT-CDR))
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(NOT-NO-DUPLICATESP-IMPLIES-MAKE-SIMPLE-CYCLE-AUX
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(PATH-P-IMPLIES-MAKE-SIMPLE-CYCLE-AUX-PATHP
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 (125 125 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (115 7 (:REWRITE NOT-NO-DUPLICATESP-IMPLIES-MAKE-SIMPLE-CYCLE-AUX))
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 (25 25 (:TYPE-PRESCRIPTION NO-DUPLICATESP-EQUAL))
 (7 7 (:REWRITE NOT-MAKE-SIMPLE-CYCLE-AUX-IMPLIES-DISJOINTP))
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(PATH-P-ONE-ELEMENT
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 (5 5 (:REWRITE DEFAULT-CAR))
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 (1 1 (:REWRITE DEFAULT-<-1))
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(CAR-MAKE-SIMPLE-CYCLE-AUX
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(MEMBER-MAP-NFIX-2
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 (39 39 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (39 39 (:META CANCEL_PLUS-EQUAL-CORRECT))
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 (17 17 (:REWRITE DEFAULT-<-1))
 (17 17 (:META CANCEL_PLUS-LESSP-CORRECT))
 (15 15 (:TYPE-PRESCRIPTION NATP))
 (15 15 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
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(UNTIL-FIRST-REPETITION)
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 (439 286 (:REWRITE NATP-RW))
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(SIMPLE-CYCLE-FROM-CYCLE)
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(NO-DUPLICATESP-MEMBER
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(FIRST-AND-LAST-MEMBER
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 (326 326 (:REWRITE DEFAULT-+-1))
 (220 220 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (171 171 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (171 171 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (146 73 (:TYPE-PRESCRIPTION TRUE-LISTP-APPEND))
 (122 2 (:REWRITE BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2))
 (116 2 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (104 104 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (73 73 (:TYPE-PRESCRIPTION BINARY-APPEND))
 (36 2 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (22 22 (:TYPE-PRESCRIPTION BOUNDED-TERM-GRAPH-P))
 (10 10 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (4 4 (:REWRITE NATP-RW))
 (4 4 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:TYPE-PRESCRIPTION EQLABLEP))
 )
(DAG-P-AUX-MEMBER
 (4227 250 (:REWRITE NTH-NON-NIL))
 (1621 146 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (1495 1495 (:TYPE-PRESCRIPTION LEN))
 (1277 236 (:DEFINITION TRUE-LISTP))
 (1225 245 (:DEFINITION LEN))
 (889 889 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (857 857 (:REWRITE DEFAULT-CDR))
 (615 370 (:REWRITE DEFAULT-+-2))
 (607 356 (:REWRITE DEFAULT-<-2))
 (598 356 (:REWRITE DEFAULT-<-1))
 (579 579 (:REWRITE DEFAULT-CAR))
 (500 500 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (370 370 (:REWRITE DEFAULT-+-1))
 (356 356 (:META CANCEL_PLUS-LESSP-CORRECT))
 (250 250 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (199 199 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (199 199 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (183 3 (:REWRITE BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2))
 (174 3 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (117 117 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (54 3 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (33 33 (:TYPE-PRESCRIPTION BOUNDED-TERM-GRAPH-P))
 (15 15 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (6 6 (:REWRITE NATP-RW))
 (6 6 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 (3 3 (:TYPE-PRESCRIPTION NATP))
 (3 3 (:TYPE-PRESCRIPTION EQLABLEP))
 )
(DAG-P-AUX-SUBSETP-LEMMA
 (66 4 (:REWRITE NTH-NON-NIL))
 (54 2 (:DEFINITION NTH))
 (52 7 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (37 7 (:DEFINITION TRUE-LISTP))
 (29 29 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (24 24 (:TYPE-PRESCRIPTION LEN))
 (20 20 (:REWRITE DEFAULT-CDR))
 (20 4 (:DEFINITION LEN))
 (14 2 (:DEFINITION MEMBER-EQUAL))
 (10 6 (:REWRITE DEFAULT-+-2))
 (9 9 (:REWRITE DEFAULT-CAR))
 (9 5 (:REWRITE DEFAULT-<-2))
 (9 5 (:REWRITE DEFAULT-<-1))
 (8 8 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (6 6 (:REWRITE DEFAULT-+-1))
 (6 2 (:REWRITE ZP-OPEN))
 (5 5 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 4 (:TYPE-PRESCRIPTION NFIX))
 (4 4 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (4 4 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (4 4 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 )
(DAG-P-AUX-SUBSETP
 (492 30 (:REWRITE NTH-NON-NIL))
 (439 49 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (435 15 (:DEFINITION NTH))
 (315 60 (:DEFINITION TRUE-LISTP))
 (255 255 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (177 177 (:TYPE-PRESCRIPTION LEN))
 (169 169 (:REWRITE DEFAULT-CDR))
 (150 30 (:DEFINITION LEN))
 (81 81 (:REWRITE DEFAULT-CAR))
 (75 45 (:REWRITE DEFAULT-<-2))
 (75 45 (:REWRITE DEFAULT-<-1))
 (75 45 (:REWRITE DEFAULT-+-2))
 (75 15 (:REWRITE ZP-OPEN))
 (60 60 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (45 45 (:REWRITE DEFAULT-+-1))
 (45 45 (:META CANCEL_PLUS-LESSP-CORRECT))
 (41 41 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (41 41 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (30 30 (:TYPE-PRESCRIPTION NFIX))
 (30 30 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (15 15 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (15 15 (:REWRITE CDR-CONS))
 (10 10 (:REWRITE SUBSETP-TRANSITIVE))
 )
(NEIGHBORS-EMPTY-GRAPH
 (7 1 (:REWRITE NTH-NON-NIL))
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:TYPE-PRESCRIPTION LEN))
 (1 1 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE DEFAULT-<-2))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 (1 1 (:DEFINITION LEN))
 )
(DAG-P-AUX-NOT-CONSP-GRAPH
 (242 22 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (188 35 (:DEFINITION TRUE-LISTP))
 (136 136 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (78 78 (:REWRITE DEFAULT-CDR))
 (70 70 (:REWRITE DEFAULT-CAR))
 (40 22 (:REWRITE DAG-P-AUX-SUBSETP))
 (28 4 (:REWRITE NTH-NON-NIL))
 (25 25 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (25 25 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (16 1 (:DEFINITION SUBSETP-EQUAL))
 (14 14 (:REWRITE CDR-CONS))
 (8 4 (:REWRITE DEFAULT-<-1))
 (7 7 (:REWRITE NEIGHBORS-EMPTY-GRAPH))
 (4 4 (:TYPE-PRESCRIPTION LEN))
 (4 4 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:REWRITE DEFAULT-<-2))
 (4 4 (:META CANCEL_PLUS-LESSP-CORRECT))
 (4 4 (:DEFINITION LEN))
 (2 2 (:TYPE-PRESCRIPTION NEIGHBORS))
 (2 2 (:REWRITE SUBSETP-TRANSITIVE))
 (1 1 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (1 1 (:REWRITE SUBSETP-REFLEXIVE))
 (1 1 (:REWRITE CAR-CONS))
 )
(LIST-OF-NON-NATP)
(NEIGHBORS-NON-NATP
 (25 2 (:REWRITE NTH-NON-NIL))
 (10 10 (:TYPE-PRESCRIPTION LEN))
 (10 2 (:DEFINITION LEN))
 (4 4 (:REWRITE DEFAULT-CDR))
 (4 2 (:REWRITE DEFAULT-+-2))
 (2 2 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (2 2 (:REWRITE DEFAULT-CAR))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (2 2 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (1 1 (:REWRITE POSITIVE-LEN))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(DAG-P-AUX-NON-NATP-NODES-LEMMA
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 (2617 486 (:DEFINITION TRUE-LISTP))
 (1773 1773 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (1670 1670 (:REWRITE DEFAULT-CDR))
 (1403 1403 (:REWRITE DEFAULT-CAR))
 (896 604 (:REWRITE DEFAULT-<-2))
 (861 501 (:REWRITE DEFAULT-+-2))
 (790 604 (:REWRITE DEFAULT-<-1))
 (705 141 (:REWRITE ZP-OPEN))
 (604 604 (:META CANCEL_PLUS-LESSP-CORRECT))
 (564 564 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (501 501 (:REWRITE DEFAULT-+-1))
 (476 476 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (476 476 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (362 362 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (131 54 (:REWRITE NATP-RW))
 (90 90 (:REWRITE SUBSETP-TRANSITIVE))
 (84 4 (:REWRITE DISJOINTP-CONMUTATIVE))
 (77 77 (:TYPE-PRESCRIPTION NATP))
 (68 68 (:REWRITE POSITIVE-LEN))
 (45 45 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (39 1 (:REWRITE BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2))
 (38 6 (:DEFINITION MAP-NFIX))
 (36 1 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (9 9 (:TYPE-PRESCRIPTION BOUNDED-TERM-GRAPH-P))
 (8 1 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (4 4 (:REWRITE SUBSETP-REFLEXIVE))
 (1 1 (:TYPE-PRESCRIPTION EQLABLEP))
 (1 1 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 )
(DAG-P-AUX-NON-NATP-NODES
 (302 4 (:DEFINITION DAG-P-AUX))
 (127 17 (:DEFINITION MEMBER-EQUAL))
 (75 9 (:DEFINITION MAP-NFIX))
 (42 42 (:REWRITE DEFAULT-CDR))
 (40 10 (:DEFINITION NFIX))
 (37 37 (:REWRITE DEFAULT-CAR))
 (29 3 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (21 4 (:DEFINITION TRUE-LISTP))
 (17 17 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (17 17 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (17 17 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (12 12 (:TYPE-PRESCRIPTION NEIGHBORS))
 (11 8 (:REWRITE NEIGHBORS-NON-NATP))
 (10 10 (:REWRITE DEFAULT-<-2))
 (10 10 (:REWRITE DEFAULT-<-1))
 (10 10 (:META CANCEL_PLUS-LESSP-CORRECT))
 (8 2 (:DEFINITION LIST-OF-NON-NATP))
 (4 2 (:REWRITE DEFAULT-+-2))
 (3 3 (:REWRITE SUBSETP-TRANSITIVE))
 (3 3 (:REWRITE NATP-RW))
 (3 3 (:REWRITE CDR-CONS))
 (2 2 (:TYPE-PRESCRIPTION NATP))
 (2 2 (:TYPE-PRESCRIPTION LIST-OF-N))
 (2 2 (:REWRITE DEFAULT-+-1))
 (2 2 (:REWRITE CAR-CONS))
 )
(LIST-OF-GREATER-NATP)
(NEIGHBORS-GREATER-NATP
 (5 1 (:DEFINITION LEN))
 (2 1 (:REWRITE DEFAULT-<-2))
 (2 1 (:REWRITE DEFAULT-+-2))
 (1 1 (:REWRITE NATP-RW))
 (1 1 (:REWRITE DEFAULT-CDR))
 (1 1 (:REWRITE DEFAULT-<-1))
 (1 1 (:REWRITE DEFAULT-+-1))
 (1 1 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(DAG-P-AUX-GREATER-NATP-NODES
 (4305 146 (:DEFINITION NTH))
 (2555 511 (:DEFINITION LEN))
 (1570 141 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (1492 341 (:REWRITE DAG-P-AUX-SUBSETP))
 (1420 1420 (:REWRITE DEFAULT-CDR))
 (1221 227 (:DEFINITION TRUE-LISTP))
 (1168 657 (:REWRITE DEFAULT-+-2))
 (1104 1104 (:REWRITE DEFAULT-CAR))
 (988 62 (:DEFINITION SUBSETP-EQUAL))
 (877 877 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (850 501 (:REWRITE DEFAULT-<-2))
 (790 501 (:REWRITE DEFAULT-<-1))
 (730 146 (:REWRITE ZP-OPEN))
 (657 657 (:REWRITE DEFAULT-+-1))
 (584 584 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (501 501 (:META CANCEL_PLUS-LESSP-CORRECT))
 (369 369 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (369 369 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (358 358 (:TYPE-PRESCRIPTION LIST-OF-N))
 (341 341 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (329 89 (:REWRITE NEIGHBORS-GREATER-NATP))
 (292 292 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (219 137 (:REWRITE NATP-RW))
 (211 211 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (200 4 (:REWRITE BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2))
 (199 19 (:REWRITE BOUNDED-NATP-LIST-OF-N))
 (188 4 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (176 176 (:TYPE-PRESCRIPTION NATP))
 (161 19 (:DEFINITION BOUNDED-NATP))
 (143 143 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (104 104 (:REWRITE SUBSETP-TRANSITIVE))
 (92 14 (:REWRITE SUBSETP-CONS))
 (52 4 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (40 40 (:TYPE-PRESCRIPTION BOUNDED-TERM-GRAPH-P))
 (36 36 (:TYPE-PRESCRIPTION NEIGHBORS))
 (22 2 (:REWRITE MAP-NFIX-MEMBER))
 (10 10 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (4 4 (:TYPE-PRESCRIPTION EQLABLEP))
 (4 4 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 (3 3 (:REWRITE SUBSETP-REFLEXIVE))
 )
(GREATER-NATP-NODES)
(LIST-OF-GREATER-NATP-GREATER-NATP-NODES
 (34 32 (:REWRITE DEFAULT-CAR))
 (28 14 (:REWRITE DEFAULT-<-2))
 (15 14 (:REWRITE DEFAULT-CDR))
 (14 14 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (14 14 (:REWRITE DEFAULT-<-1))
 (14 14 (:META CANCEL_PLUS-LESSP-CORRECT))
 (12 12 (:REWRITE NATP-RW))
 )
(NON-NATP-NODES)
(LIST-OF-NON-NATP-NON-NATP-NODES
 (16 15 (:REWRITE DEFAULT-CAR))
 (11 10 (:REWRITE DEFAULT-CDR))
 (9 9 (:REWRITE NATP-RW))
 )
(NODES-SUBSETP
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 (1413 1362 (:REWRITE DEFAULT-CDR))
 (383 383 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (383 383 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (242 242 (:REWRITE NATP-RW))
 (158 158 (:REWRITE DEFAULT-<-2))
 (158 158 (:REWRITE DEFAULT-<-1))
 (158 158 (:META CANCEL_PLUS-LESSP-CORRECT))
 )
(DAG-P-MAIN-PROPERTY
 (362 20 (:REWRITE NTH-NON-NIL))
 (310 10 (:DEFINITION NTH))
 (275 55 (:DEFINITION LEN))
 (143 5 (:DEFINITION LIST-OF-GREATER-NATP))
 (120 65 (:REWRITE DEFAULT-+-2))
 (117 117 (:REWRITE DEFAULT-CDR))
 (67 67 (:REWRITE DEFAULT-CAR))
 (66 38 (:REWRITE DEFAULT-<-2))
 (65 65 (:REWRITE DEFAULT-+-1))
 (65 4 (:DEFINITION LIST-OF-NON-NATP))
 (58 38 (:REWRITE DEFAULT-<-1))
 (50 50 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (50 10 (:REWRITE ZP-OPEN))
 (45 3 (:DEFINITION GREATER-NATP-NODES))
 (40 40 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (40 10 (:REWRITE NEIGHBORS-GREATER-NATP))
 (38 38 (:META CANCEL_PLUS-LESSP-CORRECT))
 (30 6 (:DEFINITION BINARY-APPEND))
 (29 29 (:TYPE-PRESCRIPTION NATP))
 (25 25 (:REWRITE NATP-RW))
 (20 20 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (18 3 (:DEFINITION NON-NATP-NODES))
 (15 15 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (10 10 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (10 10 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (10 10 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (10 2 (:DEFINITION MAP-NFIX))
 (1 1 (:REWRITE DAG-P-COMPLETENESS))
 )
(DAG-NODES-AUX-INDEPENDENT-OF-PATH
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 (8510 289 (:DEFINITION NTH))
 (8011 534 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (7988 534 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (4155 831 (:DEFINITION LEN))
 (3594 3594 (:TYPE-PRESCRIPTION LEN))
 (2313 1276 (:REWRITE DEFAULT-+-2))
 (2105 2105 (:REWRITE DEFAULT-CDR))
 (1583 1583 (:REWRITE DEFAULT-CAR))
 (1470 893 (:REWRITE DEFAULT-<-2))
 (1445 289 (:REWRITE ZP-OPEN))
 (1443 893 (:REWRITE DEFAULT-<-1))
 (1382 1276 (:REWRITE DEFAULT-+-1))
 (1156 1156 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (1104 97 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (1015 157 (:REWRITE NEIGHBORS-GREATER-NATP))
 (900 18 (:REWRITE BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2))
 (893 893 (:META CANCEL_PLUS-LESSP-CORRECT))
 (863 160 (:DEFINITION TRUE-LISTP))
 (846 18 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (611 611 (:TYPE-PRESCRIPTION TRUE-LISTP))
 (610 610 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (603 603 (:TYPE-PRESCRIPTION LIST-OF-N))
 (578 578 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (562 193 (:REWRITE NATP-RW))
 (534 534 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (332 332 (:TYPE-PRESCRIPTION NATP))
 (261 261 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (234 18 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (180 180 (:TYPE-PRESCRIPTION BOUNDED-TERM-GRAPH-P))
 (135 135 (:REWRITE CDR-CONS))
 (81 81 (:REWRITE CAR-CONS))
 (50 50 (:REWRITE FOLD-CONSTS-IN-+))
 (45 45 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (27 27 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 (18 18 (:TYPE-PRESCRIPTION EQLABLEP))
 (7 7 (:REWRITE SUBSETP-TRANSITIVE))
 (3 3 (:REWRITE EQUAL-CONSTANT-+))
 )
(DAG-NODES-AUX-SUBSETP-REWRITE-RULE
 (222 2 (:DEFINITION DAG-P-AUX))
 (198 4 (:DEFINITION NEIGHBORS))
 (153 7 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (151 2 (:DEFINITION DAG-NODES-AUX))
 (134 8 (:REWRITE NTH-NON-NIL))
 (130 7 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (118 4 (:DEFINITION NTH))
 (54 3 (:DEFINITION SUBSETP-EQUAL))
 (52 7 (:DEFINITION MEMBER-EQUAL))
 (50 10 (:DEFINITION LEN))
 (48 48 (:TYPE-PRESCRIPTION LEN))
 (38 20 (:REWRITE DEFAULT-+-2))
 (31 31 (:REWRITE DEFAULT-CDR))
 (26 26 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (24 20 (:REWRITE DEFAULT-+-1))
 (21 21 (:REWRITE DEFAULT-CAR))
 (20 12 (:REWRITE DEFAULT-<-2))
 (20 12 (:REWRITE DEFAULT-<-1))
 (20 4 (:REWRITE ZP-OPEN))
 (16 16 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (16 4 (:REWRITE NEIGHBORS-GREATER-NATP))
 (13 13 (:TYPE-PRESCRIPTION LIST-OF-N))
 (12 12 (:META CANCEL_PLUS-LESSP-CORRECT))
 (10 10 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (10 10 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (10 2 (:REWRITE COMMUTATIVITY-OF-+))
 (8 8 (:TYPE-PRESCRIPTION NATP))
 (8 8 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (7 7 (:REWRITE SUBSETP-TRANSITIVE))
 (7 7 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (6 6 (:TYPE-PRESCRIPTION NFIX))
 (4 4 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (4 4 (:REWRITE NATP-RW))
 (2 2 (:REWRITE FOLD-CONSTS-IN-+))
 )
(MEASURE-REC-DAG-ORDINALP
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 (1130 62 (:REWRITE DAG-P-MAIN-PROPERTY))
 (1001 83 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (938 19 (:DEFINITION NEIGHBORS))
 (865 83 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (642 38 (:REWRITE NTH-NON-NIL))
 (558 19 (:DEFINITION NTH))
 (525 105 (:DEFINITION LEN))
 (484 4 (:REWRITE DAG-NODES-AUX-SUBSETP-REWRITE-RULE))
 (349 182 (:REWRITE DEFAULT-+-2))
 (336 336 (:TYPE-PRESCRIPTION LEN))
 (330 6 (:DEFINITION ACL2-COUNT))
 (286 4 (:DEFINITION DAG-NODES-AUX))
 (208 182 (:REWRITE DEFAULT-+-1))
 (205 199 (:REWRITE DEFAULT-CDR))
 (184 8 (:DEFINITION LIST-OF-GREATER-NATP))
 (141 125 (:REWRITE DEFAULT-CAR))
 (128 128 (:TYPE-PRESCRIPTION LIST-OF-N))
 (125 77 (:REWRITE DEFAULT-<-2))
 (117 77 (:REWRITE DEFAULT-<-1))
 (107 83 (:REWRITE DAG-P-AUX-SUBSETP))
 (88 8 (:DEFINITION LIST-OF-NON-NATP))
 (87 19 (:REWRITE ZP-OPEN))
 (83 83 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (77 77 (:META CANCEL_PLUS-LESSP-CORRECT))
 (76 76 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (76 19 (:REWRITE NEIGHBORS-GREATER-NATP))
 (68 16 (:REWRITE COMMUTATIVITY-OF-+))
 (62 62 (:TYPE-PRESCRIPTION DAG-P))
 (60 12 (:DEFINITION INTEGER-ABS))
 (56 56 (:TYPE-PRESCRIPTION NATP))
 (54 1 (:DEFINITION O<))
 (48 6 (:DEFINITION LENGTH))
 (40 40 (:TYPE-PRESCRIPTION LIST-OF-NON-NATP))
 (40 40 (:TYPE-PRESCRIPTION LIST-OF-GREATER-NATP))
 (38 38 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (36 36 (:REWRITE NATP-RW))
 (23 23 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (22 22 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (22 22 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (19 19 (:DEFINITION MEMBER-EQUAL))
 (16 16 (:REWRITE FOLD-CONSTS-IN-+))
 (12 12 (:REWRITE DEFAULT-UNARY-MINUS))
 (9 9 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (8 8 (:TYPE-PRESCRIPTION SUBSETP-EQUAL))
 (8 8 (:REWRITE SUBSETP-TRANSITIVE))
 (8 8 (:REWRITE SUBSETP-REFLEXIVE))
 (6 6 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (6 6 (:REWRITE INTEGERP==>DENOMINATOR=1))
 (6 6 (:REWRITE DEFAULT-REALPART))
 (6 6 (:REWRITE DEFAULT-NUMERATOR))
 (6 6 (:REWRITE DEFAULT-IMAGPART))
 (6 6 (:REWRITE DEFAULT-DENOMINATOR))
 (6 6 (:REWRITE DEFAULT-COERCE-2))
 (6 6 (:REWRITE DEFAULT-COERCE-1))
 (4 1 (:REWRITE NATP-POSP))
 (1 1 (:REWRITE POSP-RW))
 (1 1 (:REWRITE DAG-P-COMPLETENESS))
 )
(DAG-RECURSION-CASE-1-LEMMA
 (264 28 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (264 28 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (237 14 (:REWRITE NTH-NON-NIL))
 (205 7 (:DEFINITION NTH))
 (140 28 (:DEFINITION LEN))
 (92 92 (:TYPE-PRESCRIPTION LEN))
 (63 35 (:REWRITE DEFAULT-+-2))
 (48 48 (:REWRITE DEFAULT-CDR))
 (35 35 (:REWRITE DEFAULT-+-1))
 (34 20 (:REWRITE DEFAULT-<-2))
 (34 20 (:REWRITE DEFAULT-<-1))
 (31 7 (:REWRITE ZP-OPEN))
 (28 28 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (28 28 (:REWRITE DAG-P-AUX-SUBSETP))
 (28 28 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (28 7 (:REWRITE NEIGHBORS-GREATER-NATP))
 (21 21 (:REWRITE DEFAULT-CAR))
 (20 20 (:META CANCEL_PLUS-LESSP-CORRECT))
 (14 14 (:TYPE-PRESCRIPTION NATP))
 (14 14 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (8 8 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (7 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:REWRITE NATP-RW))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 )
(DAG-RECURSION-CASE-1
 (385 21 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (303 20 (:REWRITE NTH-NON-NIL))
 (300 3 (:DEFINITION DAG-P-AUX))
 (273 10 (:DEFINITION NTH))
 (249 21 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (215 43 (:DEFINITION LEN))
 (184 184 (:TYPE-PRESCRIPTION LEN))
 (184 8 (:DEFINITION LIST-OF-GREATER-NATP))
 (156 82 (:REWRITE DEFAULT-+-2))
 (156 18 (:REWRITE DAG-P-MAIN-PROPERTY))
 (110 2 (:DEFINITION ACL2-COUNT))
 (95 91 (:REWRITE DEFAULT-CDR))
 (95 82 (:REWRITE DEFAULT-+-1))
 (88 8 (:DEFINITION LIST-OF-NON-NATP))
 (70 70 (:TYPE-PRESCRIPTION LIST-OF-N))
 (66 58 (:REWRITE DEFAULT-CAR))
 (61 35 (:REWRITE DEFAULT-<-2))
 (53 35 (:REWRITE DEFAULT-<-1))
 (40 40 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (40 40 (:TYPE-PRESCRIPTION LIST-OF-NON-NATP))
 (40 40 (:TYPE-PRESCRIPTION LIST-OF-GREATER-NATP))
 (30 30 (:TYPE-PRESCRIPTION NATP))
 (30 10 (:REWRITE ZP-OPEN))
 (28 7 (:REWRITE NEIGHBORS-GREATER-NATP))
 (23 23 (:REWRITE NATP-RW))
 (21 21 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (20 20 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (20 4 (:DEFINITION INTEGER-ABS))
 (16 2 (:DEFINITION LENGTH))
 (8 8 (:REWRITE SUBSETP-TRANSITIVE))
 (8 8 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (4 4 (:REWRITE DEFAULT-UNARY-MINUS))
 (3 3 (:REWRITE DAG-P-COMPLETENESS))
 (3 3 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (2 2 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (2 2 (:REWRITE INTEGERP==>DENOMINATOR=1))
 (2 2 (:REWRITE DEFAULT-REALPART))
 (2 2 (:REWRITE DEFAULT-NUMERATOR))
 (2 2 (:REWRITE DEFAULT-IMAGPART))
 (2 2 (:REWRITE DEFAULT-DENOMINATOR))
 (2 2 (:REWRITE DEFAULT-COERCE-2))
 (2 2 (:REWRITE DEFAULT-COERCE-1))
 )
(DAG-RECURSION-CASE-2-LEMMA
 (264 28 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (264 28 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (237 14 (:REWRITE NTH-NON-NIL))
 (205 7 (:DEFINITION NTH))
 (140 28 (:DEFINITION LEN))
 (92 92 (:TYPE-PRESCRIPTION LEN))
 (63 35 (:REWRITE DEFAULT-+-2))
 (47 47 (:REWRITE DEFAULT-CDR))
 (35 35 (:REWRITE DEFAULT-+-1))
 (34 20 (:REWRITE DEFAULT-<-2))
 (34 20 (:REWRITE DEFAULT-<-1))
 (31 7 (:REWRITE ZP-OPEN))
 (28 28 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (28 28 (:REWRITE DAG-P-AUX-SUBSETP))
 (28 28 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (28 7 (:REWRITE NEIGHBORS-GREATER-NATP))
 (21 21 (:REWRITE DEFAULT-CAR))
 (20 20 (:META CANCEL_PLUS-LESSP-CORRECT))
 (14 14 (:TYPE-PRESCRIPTION NATP))
 (14 14 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (8 8 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (7 7 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (7 7 (:REWRITE NATP-RW))
 (6 6 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (6 6 (:META CANCEL_PLUS-EQUAL-CORRECT))
 (2 2 (:REWRITE DAG-P-COMPLETENESS))
 )
(DAG-RECURSION-CASE-2
 (394 18 (:REWRITE NTH-NON-NIL))
 (385 21 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (300 3 (:DEFINITION DAG-P-AUX))
 (250 9 (:DEFINITION NTH))
 (249 21 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (239 5 (:REWRITE BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2))
 (224 5 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (200 40 (:DEFINITION LEN))
 (197 197 (:TYPE-PRESCRIPTION LEN))
 (184 8 (:DEFINITION LIST-OF-GREATER-NATP))
 (156 18 (:REWRITE DAG-P-MAIN-PROPERTY))
 (135 71 (:REWRITE DEFAULT-+-2))
 (115 111 (:REWRITE DEFAULT-CDR))
 (115 33 (:REWRITE NATP-RW))
 (114 7 (:REWRITE NEIGHBORS-GREATER-NATP))
 (111 106 (:REWRITE DEFAULT-CAR))
 (88 8 (:DEFINITION LIST-OF-NON-NATP))
 (81 71 (:REWRITE DEFAULT-+-1))
 (72 44 (:REWRITE DEFAULT-<-2))
 (70 70 (:TYPE-PRESCRIPTION LIST-OF-N))
 (60 5 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (58 44 (:REWRITE DEFAULT-<-1))
 (49 49 (:TYPE-PRESCRIPTION BOUNDED-TERM-GRAPH-P))
 (40 40 (:TYPE-PRESCRIPTION LIST-OF-NON-NATP))
 (40 40 (:TYPE-PRESCRIPTION LIST-OF-GREATER-NATP))
 (36 36 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (35 35 (:TYPE-PRESCRIPTION NATP))
 (29 9 (:REWRITE ZP-OPEN))
 (21 21 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (18 18 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (11 11 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (10 10 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (8 8 (:REWRITE SUBSETP-TRANSITIVE))
 (8 1 (:DEFINITION LENGTH))
 (6 6 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 (5 5 (:TYPE-PRESCRIPTION EQLABLEP))
 (5 5 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (3 3 (:REWRITE DEFAULT-UNARY-MINUS))
 (3 3 (:REWRITE DAG-P-COMPLETENESS))
 (3 3 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (1 1 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (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))
 )
(DAG-RECURSION-CASE-3
 (9174 520 (:REWRITE NTH-NON-NIL))
 (7621 260 (:DEFINITION NTH))
 (5959 417 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (5160 417 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (4345 869 (:DEFINITION LEN))
 (3774 3774 (:TYPE-PRESCRIPTION LEN))
 (3400 193 (:REWRITE DAG-P-MAIN-PROPERTY))
 (2914 1552 (:REWRITE DEFAULT-+-2))
 (1834 1826 (:REWRITE DEFAULT-CDR))
 (1755 1552 (:REWRITE DEFAULT-+-1))
 (1523 936 (:REWRITE DEFAULT-<-2))
 (1435 936 (:REWRITE DEFAULT-<-1))
 (1362 1353 (:REWRITE DEFAULT-CAR))
 (1300 260 (:REWRITE ZP-OPEN))
 (1230 1230 (:TYPE-PRESCRIPTION NFIX))
 (1200 24 (:REWRITE BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-2))
 (1128 24 (:DEFINITION BOUNDED-TERM-GRAPH-P))
 (1081 47 (:DEFINITION LIST-OF-GREATER-NATP))
 (1052 134 (:REWRITE NEIGHBORS-GREATER-NATP))
 (1040 1040 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (777 3 (:LINEAR ACL2-COUNT-CAR-CDR-LINEAR))
 (768 276 (:REWRITE NATP-RW))
 (667 667 (:TYPE-PRESCRIPTION LIST-OF-N))
 (520 520 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (517 47 (:DEFINITION LIST-OF-NON-NATP))
 (417 417 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (386 386 (:TYPE-PRESCRIPTION NATP))
 (346 346 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (312 24 (:DEFINITION BOUNDED-NAT-TRUE-LISTP))
 (260 52 (:DEFINITION INTEGER-ABS))
 (240 240 (:TYPE-PRESCRIPTION BOUNDED-TERM-GRAPH-P))
 (236 236 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (235 235 (:TYPE-PRESCRIPTION LIST-OF-NON-NATP))
 (235 235 (:TYPE-PRESCRIPTION LIST-OF-GREATER-NATP))
 (208 26 (:DEFINITION LENGTH))
 (90 90 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (60 60 (:TYPE-PRESCRIPTION BOUNDED-NAT-TRUE-LISTP))
 (52 52 (:REWRITE DEFAULT-UNARY-MINUS))
 (47 47 (:REWRITE SUBSETP-TRANSITIVE))
 (36 36 (:LINEAR BOUNDED-TERM-GRAPH-P-NTH-PROPERTY-1))
 (26 26 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (26 26 (:REWRITE INTEGERP==>DENOMINATOR=1))
 (26 26 (:REWRITE DEFAULT-REALPART))
 (26 26 (:REWRITE DEFAULT-NUMERATOR))
 (26 26 (:REWRITE DEFAULT-IMAGPART))
 (26 26 (:REWRITE DEFAULT-DENOMINATOR))
 (26 26 (:REWRITE DEFAULT-COERCE-2))
 (26 26 (:REWRITE DEFAULT-COERCE-1))
 (24 24 (:TYPE-PRESCRIPTION EQLABLEP))
 (21 21 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (3 3 (:REWRITE DAG-P-COMPLETENESS))
 (2 2 (:REWRITE EQUAL-CONSTANT-+))
 )
(DAG-RECURSION-CASE-4
 (2098 128 (:REWRITE NTH-NON-NIL))
 (1978 6 (:REWRITE DAG-NODES-AUX-SUBSETP-REWRITE-RULE))
 (1863 64 (:DEFINITION NTH))
 (1852 9 (:DEFINITION DAG-P-AUX))
 (844 844 (:TYPE-PRESCRIPTION LEN))
 (835 167 (:DEFINITION LEN))
 (719 43 (:REWRITE DAG-P-AUX-GREATER-NATP-NODES))
 (583 43 (:REWRITE DAG-P-AUX-NON-NATP-NODES))
 (478 266 (:REWRITE DEFAULT-+-2))
 (338 202 (:REWRITE DEFAULT-<-2))
 (329 202 (:REWRITE DEFAULT-<-1))
 (325 319 (:REWRITE DEFAULT-CDR))
 (320 64 (:REWRITE ZP-OPEN))
 (284 266 (:REWRITE DEFAULT-+-1))
 (256 256 (:TYPE-PRESCRIPTION |x < y  =>  0 < -x+y|))
 (228 219 (:REWRITE DEFAULT-CAR))
 (184 8 (:DEFINITION LIST-OF-GREATER-NATP))
 (174 174 (:TYPE-PRESCRIPTION NFIX))
 (156 18 (:REWRITE DAG-P-MAIN-PROPERTY))
 (128 128 (:REWRITE TERM-GRAPH-P-MAIN-PROPERTY))
 (90 90 (:TYPE-PRESCRIPTION LIST-OF-N))
 (88 8 (:DEFINITION LIST-OF-NON-NATP))
 (67 2 (:DEFINITION ACL2-COUNT))
 (64 16 (:REWRITE NEIGHBORS-GREATER-NATP))
 (63 63 (:REWRITE RATIONALP-IMPLIES-ACL2-NUMBERP))
 (53 53 (:META CANCEL_TIMES-EQUAL-CORRECT))
 (48 48 (:TYPE-PRESCRIPTION NATP))
 (43 43 (:REWRITE DAG-P-AUX-NOT-CONSP-GRAPH))
 (40 40 (:TYPE-PRESCRIPTION LIST-OF-NON-NATP))
 (40 40 (:TYPE-PRESCRIPTION LIST-OF-GREATER-NATP))
 (32 32 (:REWRITE NATP-RW))
 (12 12 (:TYPE-PRESCRIPTION MEMBER-EQUAL))
 (10 2 (:DEFINITION INTEGER-ABS))
 (8 8 (:REWRITE SUBSETP-TRANSITIVE))
 (8 1 (:DEFINITION LENGTH))
 (3 3 (:REWRITE DAG-P-COMPLETENESS))
 (3 3 (:REWRITE DAG-P-AUX-COMPLETENESS-MAIN-LEMMA))
 (2 2 (:REWRITE DEFAULT-UNARY-MINUS))
 (1 1 (:REWRITE NUMERATOR-WHEN-INTEGERP))
 (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))
 )
